path: root/parallel/ciancarini94comparison.ps

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>

imagemask

grestore

pse
-30 -28 xl
196 69 gm
(nc 0 0 781 538 6 rc)kp
F 1 setTxMode
1 fs
bu fc
{}mark T /Times-Bold /|______Times-Bold 0 rf
bn
18 fz
bu fc
2 F /|______Times-Bold fnt
bn
(A Comparison of Parallel Search Algorithms based on)show
213 225 gm
(Tree Splitting)show
289 227 gm
14 fz
bu fc
2 F /|______Times-Bold fnt
bn
(Paolo Ciancarini)show
410 182 gm
(Technical Report UBLCS-94-14)show
439 249 gm
0 fs
bu fc
{}mark T /Times-Roman /|______Times-Roman 0 rf
bn
bu fc
2 F /|______Times-Roman fnt
bn
(May 1994)show
633 183 gm
(Laboratory for Computer Science)show
651 215 gm
(University of Bologna)show
669 199 gm
(Piazza di Porta S. Donato, 5)show
687 216 gm
(40127 Bologna \(Italy\))show
F T cp
%%Page: ? 2
op
30 28 811 566 fr
0 0 xl
1 1 pen
0 0 gm
(nc 0 0 0 0 6 rc)kp
139 79 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0 fs
10 fz
bu fc
2 F /|______Times-Roman fnt
bn
1.17721 0. 32 0.11772 0.(The University of Bologna Laboratory for Computer Science Research Technical Reports are available via)awidthshow
153 79 gm
0.77774 0. 32 0.07777 0.(anonymous FTP from the area )awidthshow
bu fc
{}mark T /Courier /|______Courier 0 rf
bn
bu fc
2 F /|______Courier fnt
bn
0.29316 0.(ftp.cs.unibo.it:/pub/TR/UBLCS)ashow
bu fc
2 F /|______Times-Roman fnt
bn
0.91796 0. 32 0.09179 0.( in compressed PostScript format.)awidthshow
167 79 gm
1.05239 0. 32 0.10523 0.(Abstracts are available from the same host in the directory )awidthshow
bu fc
2 F /|______Courier fnt
bn
0.42799 0.(/pub/TR/UBLCS/ABSTRACTS)ashow
bu fc
2 F /|______Times-Roman fnt
bn
0.83404 0. 32 0.08340 0.( in plain text)awidthshow
181 79 gm
(format. All local authors can be reached via e-mail at the address )show
2 fs
bu fc
{}mark T /Times-Italic /|______Times-Italic 0 rf
bn
bu fc
2 F /|______Times-Italic fnt
bn
(last-name)show
0 fs
bu fc
2 F /|______Courier fnt
bn
(@cs.unibo.it.)show
207 79 gm
1 fs
11 fz
bu fc
2 F /|______Times-Bold fnt
bn
(UBLCS Technical Report Series)show
232 80 gm
0 fs
10 fz
bu fc
2 F /|______Times-Roman fnt
bn
(93-1)show
232 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
2.19955 0. 32 0.21995 0.(Consistent Global States of Distributed Systems: Fundamental Concepts and Mechanism)awidthshow
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
1.11801 0. 32 0.11180 0.(, by \205.)awidthshow
245 110 gm
(Babao)show
245 136 gm
(g;\371lu and K. Marzullo, January 1993.)show
258 80 gm
(93-2)show
258 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Understanding Non-Blocking Atomic Commitment)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, by \205. Babao)show
258 368 gm
(g;\371lu and S. Toueg, January 1993.)show
271 80 gm
(93-3)show
271 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Anchors and Paths in a Hypertext Publishing System)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, by C.  Maioli and F. Vitali, February 1993.)show
284 80 gm
(93-4)show
284 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(A Formalization of Priority Inversion)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, by \205. Babao)show
284 316 gm
(g;\371lu, K. Marzullo and F. Schneider, March 1993.)show
297 80 gm
(93-5)show
297 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
0.68313 0. 32 0.06831 0.(Some Modifications to the Dexter Model for the Formal Description of Hypertexts)awidthshow
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
0.52368 0. 32 0.05236 0.(, by S. Lamberti, C.)awidthshow
310 110 gm
(Maioli and F. Vitali, April 1993.)show
323 80 gm
(93-6)show
323 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
0.50613 0. 32 0.05061 0.(Versioning Issues in a Collaborative Distributed Hypertext)awidthshow
11 fz
bu fc
2 F /|______Times-Italic fnt
bn
( )show
323 354 gm
10 fz
bu fc
2 F /|______Times-Italic fnt
bn
0.18540 0.(System)ashow
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
0.49468 0. 32 0.04946 0.(, by C. Maioli, S. Sola and F. Vitali,)awidthshow
336 110 gm
(April 1993.)show
349 80 gm
(93-7)show
349 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Distributed Programming with Logic Tuple Spaces)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, by P. Ciancarini, April 1993.)show
362 80 gm
(93-8)show
362 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Coordinating Rule-Based Software Processes with ESP)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, by P. Ciancarini, April 1993.)show
375 80 gm
(93-9)show
375 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(What is Logic Programming good for in Software Engineering)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, by P. Ciancarini and G. Levi, April 1993.)show
388 80 gm
(93-10)show
388 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
0.84320 0. 32 0.08432 0.(Scheduling Real Time Tasks: A Performance Study)awidthshow
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
0.59097 0. 32 0.05909 0.(, by F.  Panzieri, L. Donatiello and L. Poretti, May)awidthshow
401 110 gm
(1993.)show
414 80 gm
(93-11)show
414 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
0.58334 0. 32 0.05833 0.(Specification and Detection of Behavioral Patterns in Distributed Computations)awidthshow
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
0.37704 0. 32 0.03770 0.(, by \205. Babao)awidthshow
414 498 gm
0.54534 0. 32 0.05453 0.(g;\371lu and)awidthshow
427 110 gm
(M. Raynal, May 1993.)show
440 80 gm
(93-12)show
440 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Interaction Systems II: The Practice of Optimal Reductions)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, by A. Asperti and C. Laneve, May 1993.)show
453 80 gm
(93-13)show
453 110 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
1.00616 0. 32 0.10061 0.(Reliability Analysis of Tree-Based Structures and its Application to Fault-Tolerant VLSI Systems)awidthshow
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0.61645 0. 32 0.06164 0.(, by)awidthshow
466 110 gm
(Marco Roccetti, June 1993.)show
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(Guard Compilation in Logic Shared Dataspace Languages)show
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(, by M. Garpari, June 1993.)show
492 80 gm
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1.16424 0. 32 0.11642 0.(Data Algorithm: A Numerical Method to Extract Shape Information from Gray Scale Images)awidthshow
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0.66116 0. 32 0.06611 0.(, by R.)awidthshow
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(Davoli and F. Tamburini, June 1993.)show
518 80 gm
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(Towards Performance Evaluation in Process Algebra)show
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(, by R. Gorrieri and M. Roccetti, July 1993.)show
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(Split and ST Bisimulation Semantics)show
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(, by R. Gorrieri and C. Laneve, July 1993.)show
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(Multilanguage Interoperability)show
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(, by G. Attardi and M. Gaspari, July 1993.)show
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0.20431 0. 32 0.02043 0.(HERMES: an Expert System for the Prognosis of Hepatic Diseases)awidthshow
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0.14709 0. 32 0.01470 0.(, by I. Bonf\210, C. Maioli, F. Sarti, G.L.)awidthshow
570 110 gm
(Milandri and P.R. Dal Monte, September 1993)show
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(An Information Flow Security Property for CCS)show
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(, by R. Focardi and R. Gorrieri, October 1993.)show
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(A Classification of Security Properties)show
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(, by R. Focardi and R. Gorrieri, October 1993.)show
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(Real Time Systems: A Tutorial)show
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(, by F. Panzieri and R.  Davoli, October 1993.)show
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-0.00643 0.(A Scalable Architecture for Reliable Distributed Multimedia Applications)ashow
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-0.00637 0.(, by F. Panzieri and M. Roccetti,)ashow
635 110 gm
(October 1993.)show
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(Wide-Area Distribution Issues in Hypertext Systems)show
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(, by C. Maioli, S. Sola and F. Vitali, October 1993.)show
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(On Relating Some Models for Concurrency)show
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(, by P. Degano, R. Gorrieri and S. Vigna, October 1993.)show
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1.45263 0. 32 0.14526 0.(Axiomatising ST Bisimulation Equivalence)awidthshow
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0.88378 0. 32 0.08837 0.(, by N. Busi, R. van Glabbeek and R. Gorrieri, December)awidthshow
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(1993.)show
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1.48498 0. 32 0.14849 0.(A Theory of Processes with Durational Actions)awidthshow
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1.30096 0. 32 0.13009 0.(, by R. Gorrieri, M. Roccetti and E. Stancampiano,)awidthshow
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2.25738 0. 32 0.22573 0.(A Comparison of Parallel Search Algorithms based on)awidthshow
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(Paolo Ciancarini)show
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(Technical Report UBLCS-94-14)show
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(Abstract)show
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0.01831 0. 32 0.00183 0.(We have used a distributed programming environment to compare a number of parallel search algorithms in the)awidthshow
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0.43136 0. 32 0.04313 0.(domain of chess. The environment runs on a network of workstations; it is based on Linda for coordination of)awidthshow
408 79 gm
0.84838 0. 32 0.08483 0.(the search and on GNUChess for chess knowledge. In order to make a practical comparison, we have built)awidthshow
422 79 gm
0.43441 0. 32 0.04344 0.(several parallel programs using different search algorithms. We have formalized and classified the concept of)awidthshow
436 79 gm
0.34042 0. 32 0.03404 0.(parallel search algorithms based game tree splitting. The algorithms have been classified in two main classes:)awidthshow
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0.46676 0. 32 0.04667 0.(static and dynamic. We show that on a workstation network static algorithms are more efficient than dynamic)awidthshow
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(ones. Our results confirm and broaden older works by Marsland, Campbell, Schaeffer, and others.)show
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(.)show
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(E-mail: [email protected])show
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(A Comparison of Parallel Search Algorithms)show
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(UBLCS-94-14)show
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(2)show
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(1. Introduction)show
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1.81762 0. 32 0.18176 0.(The alphabeta algorithm is the basis of most sequential programs that search game trees. Its)awidthshow
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0.35644 0. 32 0.03564 0.(efficiency is decisive in chess playing programs, whose playing strength can be precisely measured)awidthshow
169 79 gm
1.08215 0. 32 0.10821 0.(using the Elo system [Elo86]. For instance, some experiments found that improving 5 times the)awidthshow
180 79 gm
0.24139 0. 32 0.02413 0.(running time of such an algorithm the playing strength of a chess programs improves about 200 Elo)awidthshow
191 79 gm
0.08392 0. 32 0.00839 0.(points [Tho82]. One could expect that multiprocessors and multicomputers should be very helpful in)awidthshow
202 79 gm
1.07360 0. 32 0.10736 0.(building stronger chess programs. However, it is well known that the efficient parallelization of)awidthshow
213 79 gm
0.75637 0. 32 0.07563 0.(alphabeta is a difficult problem [FinFis82]. Several different ways to parallelism in chess playing)awidthshow
224 79 gm
(programs have been explored; a short survey is found in [BalVRe86]. The main methods are:)show
236 88 gm
2.15698 0. 32 0.21569 0.(i\) Parallel aspiration search [Bau78]: the alphabeta window is partitioned in a number of)awidthshow
247 101 gm
0.00518 0. 32 0.00051 0.(contiguous segments, that are used by different processors to explore the same game tree; this is)awidthshow
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(a form of OR-parallelism.)show
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1.79580 0. 32 0.17958 0.(ii\) Parallel evaluation by special hardware; )awidthshow
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0.39163 0.(e.g.)ashow
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1.88949 0. 32 0.18894 0.(, HITECH uses parallel hardware for move)awidthshow
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2.09396 0. 32 0.20939 0.(generation [Ebe86], while Deep Thought [Hsu90] uses parallel hardware for evaluating)awidthshow
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(positions.)show
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0.44219 0. 32 0.04421 0.(iii\) Mapping the search space on the processor set by a hash function: this is advantageous if the)awidthshow
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1.15493 0. 32 0.11549 0.(search space contains several duplicate states; )awidthshow
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0.24205 0.(e.g.)ashow
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1.09634 0. 32 0.10963 0.(, [Sti91] describes how the whole search)awidthshow
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(space of some chess endings was mapped on a Connection Machine.)show
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0.93551 0. 32 0.09355 0.(iv\) Parallel search of \322splitted\323 game tree: the game tree is decomposed assigning its nodes to)awidthshow
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(different search processes.)show
364 79 gm
0.66818 0. 32 0.06681 0.(The last method is the most widely studied and used. For instance, in [MarCam82] several search)awidthshow
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0.26077 0. 32 0.02607 0.(algorithms were described and compared; other experiments with different algorithms are described)awidthshow
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0.56335 0. 32 0.05633 0.(in [MOS86]. However, after those seminal papers we found no newer survey works on comparing)awidthshow
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0.09002 0. 32 0.00900 0.(parallel algorithms, although new ones have been invented. We decided to test the flexibility and the)awidthshow
408 79 gm
0.59478 0. 32 0.05947 0.(performance of a modern parallel language in implementing such algorithms on a general purpose)awidthshow
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(network.)show
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2.87628 0. 32 0.28762 0.(Thus, in this paper we compare some parallel search algorithms based on tree splitting,)awidthshow
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1.16760 0. 32 0.11676 0.(implementing them all in the same hw/sw environment, )awidthshow
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(i.e.,)show
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1.26510 0. 32 0.12651 0.( C-Linda [SCA90] on a network of)awidthshow
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0.90667 0. 32 0.09066 0.(workstations. We have developed a chess-oriented software library based on a publicly available)awidthshow
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0.73593 0. 32 0.07359 0.(program, namely GNUChess \(courtesy of Open Software Foundation\). Using these tools we have)awidthshow
474 79 gm
0.55084 0. 32 0.05508 0.(built several parallel playing programs, embedding different parallel search algorithms; in order to)awidthshow
485 79 gm
1.41540 0. 32 0.14154 0.(simplify comparison with results reported in other papers, our experiments were made using a)awidthshow
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(standard set of tests [BraKop82].)show
507 79 gm
0.30136 0. 32 0.03013 0.(This paper has the following structure: in Sect. 2 we define the concept of static and dynamic game)awidthshow
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0.22994 0. 32 0.02299 0.(tree splitting; in Sect. 3 we discuss how parallel search algorithms can be programmed in Linda; we)awidthshow
529 79 gm
0.27206 0. 32 0.02720 0.(summarise our experiments on static splitting algorithms in Sect.4, whereas Sect.5 contains data for)awidthshow
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0.39337 0. 32 0.03933 0.(dynamic splitting algorithms. In Sect.6 we make a number of comparisons with results obtained by)awidthshow
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(other researchers.)show
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0.18798 0. 32 0.01879 0.(There are several ways for handling a game tree during a parallel search, that basically differ for the)awidthshow
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0.64132 0. 32 0.06413 0.(splitting rules they use. We define some concepts in order to highlight properties of such splitting)awidthshow
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0.59432 0. 32 0.05943 0.(: Let A be a game tree and N={N)awidthshow
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0.50598 0. 32 0.05059 0.(, N)awidthshow
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0.49163 0. 32 0.04916 0.(, \311, N)awidthshow
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0.56747 0. 32 0.05674 0.(} its set of nodes; let P={P)awidthshow
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0.41320 0. 32 0.04132 0.(, P)awidthshow
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0.51040 0. 32 0.05104 0.(, \311,)awidthshow
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0.17745 0. 32 0.01774 0.(} a set of processes. A )awidthshow
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0.19348 0. 32 0.01934 0.( for A in P is a function D:N)awidthshow
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0.17547 0. 32 0.01754 0.(P which maps each node of A)awidthshow
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1.02569 0. 32 0.10256 0.(Explorer and supervisor processes)awidthshow
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0.49407 0. 32 0.04940 0.(: Let D be a splitting for the game tree A to the set P of)awidthshow
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1.24938 0. 32 0.12493 0.(processes; let N be the nodes of A and N)awidthshow
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0.36575 0. 32 0.03657 0.(N be a function that associates a)awidthshow
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0.36682 0. 32 0.03668 0.( fully identifies the subtree S)awidthshow
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0.35919 0. 32 0.03591 0.( of which it is the root, the)awidthshow
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(A Comparison of Parallel Search Algorithms)show
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(UBLCS-94-14)show
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(3)show
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(s)show
11 fz
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0.03936 0. 32 0.00393 0.( be one of N)awidthshow
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bu fc
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(i)show
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0000
0000
1000
0800
0400
0000
0000
8040
8040
8040
8040
8040
8040
8040
8040
8040
8040
4040
40C0
2140
1E40
0000
0000
>cdf
156<
0000
0000
0200
0400
0800
0000
0000
8040
8040
8040
8040
8040
8040
8040
8040
8040
8040
4040
40C0
2140
1E40
0000
0000
>cdf
155<
0000
0000
3880
4700
0000
0000
1E00
2100
4080
4080
8040
8040
8040
8040
8040
8040
4080
4080
2100
1E00
0000
0000
>cdf
154<
0000
0000
2100
2100
0000
0000
1E00
2100
4080
4080
8040
8040
8040
8040
8040
8040
4080
4080
2100
1E00
0000
0000
>cdf
153<
0000
0000
0C00
1200
2100
0000
0000
1E00
2100
4080
4080
8040
8040
8040
8040
8040
8040
4080
4080
2100
1E00
0000
0000
>cdf
152<
0000
0000
0800
0400
0200
0000
0000
1E00
2100
4080
4080
8040
8040
8040
8040
8040
8040
4080
4080
2100
1E00
0000
0000
>cdf
151<
0000
0000
0200
0400
0800
0000
0000
1E00
2100
4080
4080
8040
8040
8040
8040
8040
8040
4080
4080
2100
1E00
0000
0000
>cdf
150<
0000
0000
3880
4700
0000
0000
0000
9E00
A100
C080
8080
8040
8040
8040
8040
8040
8040
8040
8040
8040
8040
0000
0000
>cdf
149<
0000
0000
8800
8800
0000
0000
7000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
0000
0000
>cdf
148<
0000
0000
3000
4800
8400
0000
0000
7000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
0000
0000
>cdf
147<
0000
0000
8000
4000
2000
0000
0000
E000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
0000
0000
>cdf
146<
0000
0000
1000
2000
4000
0000
0000
E000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
0000
0000
>cdf
145<
0000
0000
1100
1100
0000
0000
1E00
2100
4080
4080
8040
8040
FFC0
8000
8000
8000
4000
4080
2100
1E00
0000
0000
>cdf
144<
0000
0000
0C00
1200
2100
0000
0000
1E00
2100
4080
4080
8040
8040
FFC0
8000
8000
8000
4000
4080
2100
1E00
0000
0000
>cdf
143<
0000
0000
1000
0800
0400
0000
0000
1E00
2100
4080
4080
8040
8040
FFC0
8000
8000
8000
4000
4080
2100
1E00
0000
0000
>cdf
142<
0000
0000
0200
0400
0800
0000
0000
1E00
2100
4080
4080
8040
8040
FFC0
8000
8000
8000
4000
4080
2100
1E00
0000
0000
>cdf
141<
0000
0000
1F00
2080
4040
4000
8000
8000
8000
8000
8000
8000
4000
4040
2080
1F00
0400
0600
0200
0400
0800
0000
0000
>cdf
140<
0000
0000
0E00
1100
1100
1100
0E00
0000
0000
1F00
6080
8040
0040
00C0
0340
0C40
3040
4040
8040
8040
80C0
4340
3C40
0000
0000
>cdf
139<
0000
0000
3880
4700
0000
0000
1F00
6080
8040
0040
00C0
0340
0C40
3040
4040
8040
8040
80C0
4340
3C40
0000
0000
>cdf
138<
0000
0000
1100
1100
0000
0000
1F00
6080
8040
0040
00C0
0340
0C40
3040
4040
8040
8040
80C0
4340
3C40
0000
0000
>cdf
137<
0000
0000
0C00
1200
2100
0000
0000
1F00
6080
8040
0040
00C0
0340
0C40
3040
4040
8040
8040
80C0
4340
3C40
0000
0000
>cdf
136<
0000
0000
0800
0400
0200
0000
0000
1F00
6080
8040
0040
00C0
0340
0C40
3040
4040
8040
8040
80C0
4340
3C40
0000
0000
>cdf
135<
0000
0000
0200
0400
0800
0000
0000
1F00
6080
8040
0040
00C0
0340
0C40
3040
4040
8040
8040
80C0
4340
3C40
0000
0000
>cdf
134<
0000
0000
1080
1080
0000
0000
8010
8010
8010
8010
8010
8010
8010
8010
8010
8010
8010
8010
8010
8010
4020
4020
30C0
0F00
0000
0000
>cdf
133<
0000
0000
0880
0880
0000
0000
0700
18C0
2020
4010
4010
8008
8008
8008
8008
8008
8008
8008
8008
4010
4010
2020
18C0
0700
0000
0000
>cdf
132<
0000
0000
3880
4700
0000
0000
8010
C010
C010
A010
A010
9010
8810
8810
8410
8210
8210
8110
8090
8090
8050
8030
8030
8010
0000
0000
>cdf
131<
0000
0000
0200
0400
0800
0000
FFC0
8000
8000
8000
8000
8000
8000
8000
FF00
8000
8000
8000
8000
8000
8000
8000
8000
FFC0
0000
0000
>cdf
130<
0000
0000
0FC0
3020
4010
4000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
4000
4010
3020
0FC0
0200
0300
0100
0100
0200
0000
0000
>cdf
129<
00000000
00000000
03800000
04400000
04400000
03800000
01000000
01000000
01000000
02800000
02800000
04400000
04400000
08200000
08200000
10100000
10100000
3FF80000
20080000
20080000
40040000
40040000
80020000
80020000
00000000
00000000
>cdf
128<
00000000
00000000
04400000
04400000
00000000
00000000
01000000
01000000
01000000
02800000
02800000
04400000
04400000
08200000
08200000
10100000
10100000
3FF80000
20080000
20080000
40040000
40040000
80020000
80020000
00000000
00000000
>cdf
126<
0000
0000
3810
4420
83C0
0000
0000
>cdf
125<
0000
0000
C000
2000
1000
1000
1000
1000
1000
1000
1000
1000
0800
1000
1000
1000
1000
1000
1000
1000
1000
1000
2000
C000
0000
0000
>cdf
124<
0000
0000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
0000
0000
>cdf
123<
0000
0000
1800
2000
4000
4000
4000
4000
4000
4000
4000
4000
8000
4000
4000
4000
4000
4000
4000
4000
4000
4000
2000
1800
0000
0000
>cdf
122<
0000
0000
FFC0
0040
0080
0100
0200
0200
0400
0800
1000
1000
2000
4000
8000
FFC0
0000
0000
>cdf
121<
0000
0000
8020
8020
4040
4040
4040
2080
2080
1100
1100
1100
0A00
0A00
0400
0400
0800
0800
1000
1000
2000
2000
0000
0000
>cdf
120<
0000
0000
8040
8040
4080
2100
2100
1200
0C00
0C00
1200
2100
2100
4080
8040
8040
0000
0000
>cdf
119<
00000000
00000000
80808000
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80808000
41410000
41410000
41410000
22220000
22220000
22220000
14140000
14140000
14140000
08080000
08080000
00000000
00000000
>cdf
118<
0000
0000
8020
8020
4040
4040
4040
2080
2080
1100
1100
1100
0A00
0A00
0400
0400
0000
0000
>cdf
117<
0000
0000
8040
8040
8040
8040
8040
8040
8040
8040
8040
8040
4040
40C0
2140
1E40
0000
0000
>cdf
116<
0000
0000
2000
2000
2000
2000
FE00
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
1100
0E00
0000
0000
>cdf
115<
0000
0000
3F00
4080
8040
8000
8000
4000
3F00
0080
0040
0040
0040
8040
4080
3F00
0000
0000
>cdf
114<
0000
0000
9E00
A100
C080
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
0000
0000
>cdf
113<
0000
0000
1E40
2140
40C0
4040
8040
8040
8040
8040
8040
8040
4040
40C0
2140
1E40
0040
0040
0040
0040
0000
0000
>cdf
112<
0000
0000
9E00
A100
C080
8080
8040
8040
8040
8040
8040
8040
8080
C080
A100
9E00
8000
8000
8000
8000
0000
0000
>cdf
111<
0000
0000
1E00
2100
4080
4080
8040
8040
8040
8040
8040
8040
4080
4080
2100
1E00
0000
0000
>cdf
110<
0000
0000
9E00
A100
C080
8080
8040
8040
8040
8040
8040
8040
8040
8040
8040
8040
0000
0000
>cdf
109<
00000000
00000000
9C1E0000
A2210000
C1408000
80808000
80808000
80808000
80808000
80808000
80808000
80808000
80808000
80808000
80808000
80808000
00000000
00000000
>cdf
108<
0000
0000
E000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
0000
0000
>cdf
107<
0000
0000
8000
8000
8000
8000
8080
8100
8200
8400
8800
9000
E000
9000
8800
8400
8200
8100
8080
8040
0000
0000
>cdf
106<
0000
0000
0400
0400
0000
0000
1C00
0400
0400
0400
0400
0400
0400
0400
0400
0400
0400
0400
0400
0400
0400
0400
0400
0400
8800
7000
0000
0000
>cdf
105<
0000
0000
2000
2000
0000
0000
E000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
0000
0000
>cdf
104<
0000
0000
8000
8000
8000
8000
9E00
A100
C080
8080
8040
8040
8040
8040
8040
8040
8040
8040
8040
8040
0000
0000
>cdf
103<
0000
0000
1E40
2140
40C0
4040
8040
8040
8040
8040
8040
8040
4040
40C0
2140
1E40
0040
0040
0040
4080
2100
1E00
0000
0000
>cdf
102<
0000
0000
0E00
1100
2000
2000
FC00
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
0000
0000
>cdf
101<
0000
0000
1E00
2100
4080
4080
8040
8040
FFC0
8000
8000
8000
4000
4080
2100
1E00
0000
0000
>cdf
100<
0000
0000
0040
0040
0040
0040
1E40
2140
40C0
4040
8040
8040
8040
8040
8040
8040
4040
40C0
2140
1E40
0000
0000
>cdf
99<
0000
0000
1F00
2080
4040
4000
8000
8000
8000
8000
8000
8000
4000
4040
2080
1F00
0000
0000
>cdf
98<
0000
0000
8000
8000
8000
8000
9E00
A100
C080
8080
8040
8040
8040
8040
8040
8040
8080
C080
A100
9E00
0000
0000
>cdf
97<
0000
0000
1F00
6080
8040
0040
00C0
0340
0C40
3040
4040
8040
8040
80C0
4340
3C40
0000
0000
>cdf
96<
0000
0000
8000
4000
2000
1000
0000
0000
>cdf
95<
00000000
00000000
FFFF0000
00000000
00000000
>cdf
94<
0000
0000
3000
4800
8400
0000
0000
>cdf
93<
0000
0000
F000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
F000
0000
0000
>cdf
92<
0000
0000
8000
8000
4000
4000
2000
2000
1000
1000
0800
0800
0400
0400
0200
0200
0100
0100
0080
0080
0040
0040
0000
0000
>cdf
91<
0000
0000
F000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
F000
0000
0000
>cdf
90<
0000
0000
FFC0
0040
0080
0080
0100
0200
0200
0400
0400
0800
0800
1000
2000
2000
4000
4000
8000
FFC0
0000
0000
>cdf
89<
0000
0000
8020
8020
4040
4040
2080
2080
1100
1100
0A00
0A00
0400
0400
0400
0400
0400
0400
0400
0400
0000
0000
>cdf
88<
0000
0000
8020
8020
4040
4040
2080
1100
1100
0A00
0400
0400
0A00
1100
1100
2080
4040
4040
8020
8020
0000
0000
>cdf
87<
00000000
00000000
80002000
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40404000
40404000
40404000
20A08000
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20A08000
11110000
11110000
11110000
0A0A0000
0A0A0000
0A0A0000
04040000
04040000
04040000
00000000
00000000
>cdf
86<
0000
0000
8008
8008
4010
4010
4010
2020
2020
2020
1040
1040
1040
0880
0880
0880
0500
0500
0200
0200
0000
0000
>cdf
85<
0000
0000
8010
8010
8010
8010
8010
8010
8010
8010
8010
8010
8010
8010
8010
8010
4020
4020
30C0
0F00
0000
0000
>cdf
84<
0000
0000
FFF8
0200
0200
0200
0200
0200
0200
0200
0200
0200
0200
0200
0200
0200
0200
0200
0200
0200
0000
0000
>cdf
83<
0000
0000
3F80
4040
8020
8000
8000
8000
6000
1F00
00C0
0020
0020
0010
0010
0010
8020
8020
60C0
1F00
0000
0000
>cdf
82<
0000
0000
FF00
80C0
8020
8020
8010
8010
8010
8020
8020
80C0
FF80
8080
8040
8040
8020
8020
8010
8010
0000
0000
>cdf
81<
0000
0000
0700
18C0
2020
4010
4010
8008
8008
8008
8008
8008
8008
8008
8008
4090
4050
2020
18D0
0708
0000
0000
>cdf
80<
0000
0000
FE00
8180
8040
8040
8020
8020
8020
8020
8040
8040
8180
FE00
8000
8000
8000
8000
8000
8000
0000
0000
>cdf
79<
0000
0000
0700
18C0
2020
4010
4010
8008
8008
8008
8008
8008
8008
8008
8008
4010
4010
2020
18C0
0700
0000
0000
>cdf
78<
0000
0000
8010
C010
C010
A010
A010
9010
8810
8810
8410
8210
8210
8110
8090
8090
8050
8030
8030
8010
0000
0000
>cdf
77<
00000000
00000000
80020000
C0060000
A00A0000
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88220000
84420000
82820000
81020000
80020000
80020000
80020000
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80020000
00000000
00000000
>cdf
76<
0000
0000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
FFC0
0000
0000
>cdf
75<
0000
0000
8010
8020
8040
8080
8100
8200
8400
8800
9000
A800
C400
8200
8100
8080
8040
8020
8010
8008
0000
0000
>cdf
74<
0000
0000
0010
0010
0010
0010
0010
0010
0010
0010
0010
0010
0010
0010
8010
8010
8020
4020
30C0
0F00
0000
0000
>cdf
73<
0000
0000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
0000
0000
>cdf
72<
0000
0000
8010
8010
8010
8010
8010
8010
8010
8010
FFF0
8010
8010
8010
8010
8010
8010
8010
8010
8010
0000
0000
>cdf
71<
0000
0000
0F80
3040
4020
4000
8000
8000
8000
8000
83F0
8010
8010
8010
8010
8010
4020
4020
30C0
0F00
0000
0000
>cdf
70<
0000
0000
FFC0
8000
8000
8000
8000
8000
8000
8000
FF00
8000
8000
8000
8000
8000
8000
8000
8000
8000
0000
0000
>cdf
69<
0000
0000
FFC0
8000
8000
8000
8000
8000
8000
8000
FF00
8000
8000
8000
8000
8000
8000
8000
8000
FFC0
0000
0000
>cdf
68<
0000
0000
FE00
8180
8040
8020
8020
8010
8010
8010
8010
8010
8010
8010
8010
8020
8020
8040
8180
FE00
0000
0000
>cdf
67<
0000
0000
0FC0
3020
4010
4000
8000
8000
8000
8000
8000
8000
8000
8000
8000
8000
4000
4010
3020
0FC0
0000
0000
>cdf
66<
0000
0000
FF80
8040
8020
8020
8020
8020
8040
FF80
8040
8020
8010
8010
8010
8010
8010
8020
8040
FF80
0000
0000
>cdf
65<
00000000
00000000
01000000
01000000
01000000
02800000
02800000
04400000
04400000
08200000
08200000
10100000
10100000
3FF80000
20080000
20080000
40040000
40040000
80020000
80020000
00000000
00000000
>cdf
64<
00000000
00000000
07C00000
18300000
20080000
40040000
43C40000
84220000
88220000
88220000
88220000
88220000
84640000
43980000
40000000
20000000
18000000
07C00000
00000000
00000000
>cdf
63<
0000
0000
1F80
2040
4020
8020
8020
0020
0040
0080
0100
0200
0200
0400
0400
0400
0000
0000
0400
0400
0000
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530 79 gm
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541 79 gm
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552 79 gm
0.66833 0. 32 0.06683 0.(description of a splitting should include the visit order followed by each process; this information)awidthshow
563 79 gm
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574 79 gm
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(33)show
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(\256)show
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(\256)show
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(N)show
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9 fz
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(41)show
12 fz
bu fc
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(\256)show
631 309 gm
bu fc
2 F /|______Helvetica fnt
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(N)show
9 fz
bu fc
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(23)show
12 fz
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2 F /|______Symbol fnt
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(\256)show
631 339 gm
bu fc
2 F /|______Helvetica fnt
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(N)show
631 348 gm
9 fz
bu fc
2 F /|______Helvetica fnt
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(34)show
648 228 gm
12 fz
bu fc
2 F /|______Helvetica fnt
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(P)show
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2 F /|______Helvetica fnt
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(3)show
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2 F /|______Helvetica fnt
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(: N)show
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bu fc
2 F /|______Helvetica fnt
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(32)show
12 fz
bu fc
2 F /|______Symbol fnt
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(\256)show
648 278 gm
bu fc
2 F /|______Helvetica fnt
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(N)show
648 287 gm
9 fz
bu fc
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(42)show
12 fz
bu fc
2 F /|______Symbol fnt
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(\256)show
648 309 gm
bu fc
2 F /|______Helvetica fnt
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(N)show
9 fz
bu fc
2 F /|______Helvetica fnt
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(36)show
665 228 gm
12 fz
bu fc
2 F /|______Helvetica fnt
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(P)show
9 fz
bu fc
2 F /|______Helvetica fnt
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(4)show
12 fz
bu fc
2 F /|______Helvetica fnt
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(: N)show
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bu fc
2 F /|______Helvetica fnt
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(31)show
12 fz
bu fc
2 F /|______Symbol fnt
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(\256)show
665 278 gm
bu fc
2 F /|______Helvetica fnt
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(N)show
665 287 gm
9 fz
bu fc
2 F /|______Helvetica fnt
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(21)show
(nc 598 218 671 384 6 rc)kp
0 gr
600.5 220.5 670.5 362.5 0 rc
587 77 gm
(nc 30 28 811 566 6 rc)kp
587 525 lin
699 186 gm
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bu fc
2 F /|______Times-Roman fnt
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(Fig.2)show
1 fs
bu fc
2 F /|______Times-Bold fnt
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( Splitting: evaluation order by every process)show
717 77 gm
0 gr
717 525 lin
736 79 gm
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747 79 gm
0.00778 0. 32 0.00077 0.(processes\325 relative speeds. Nevertheless, there are some synchronisation points marking the stages of)awidthshow
F T cp
%%Page: ? 6
op
30 28 811 566 fr
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(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
773 519 gm
(4)show
118 79 gm
11 fz
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0.19485 0. 32 0.01948 0.(the visit: a process can completely search a subtree S only after having received the minimax values)awidthshow
129 79 gm
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140 79 gm
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185 369 gm
(nc 172 368 240 502 6 rc)kp
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2 F /|______Helvetica fnt
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(P)show
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(: N)show
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bu fc
2 F /|______Helvetica fnt
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(33)show
12 fz
bu fc
2 F /|______Symbol fnt
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(\256)show
185 419 gm
bu fc
2 F /|______Helvetica fnt
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(N)show
185 428 gm
9 fz
bu fc
2 F /|______Helvetica fnt
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(22)show
12 fz
bu fc
2 F /|______Symbol fnt
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(\256)show
185 450 gm
bu fc
2 F /|______Helvetica fnt
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(Root)show
202 369 gm
(P)show
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(2)show
12 fz
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2 F /|______Helvetica fnt
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(: N)show
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(35)show
12 fz
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2 F /|______Symbol fnt
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(\256)show
202 419 gm
bu fc
2 F /|______Helvetica fnt
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(N)show
202 428 gm
9 fz
bu fc
2 F /|______Helvetica fnt
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(41)show
12 fz
bu fc
2 F /|______Symbol fnt
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(\256)show
202 450 gm
bu fc
2 F /|______Helvetica fnt
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(N)show
9 fz
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(23)show
12 fz
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2 F /|______Symbol fnt
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(\256)show
202 480 gm
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(N)show
202 489 gm
9 fz
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(34)show
219 369 gm
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(P)show
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(: N)show
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(32)show
12 fz
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(\256)show
219 419 gm
bu fc
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(N)show
219 428 gm
9 fz
bu fc
2 F /|______Helvetica fnt
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(42)show
12 fz
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2 F /|______Symbol fnt
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(\256)show
219 450 gm
bu fc
2 F /|______Helvetica fnt
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(N)show
9 fz
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(36)show
236 369 gm
12 fz
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(P)show
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(4)show
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(: N)show
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2 F /|______Helvetica fnt
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(31)show
12 fz
bu fc
2 F /|______Symbol fnt
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(\256)show
236 419 gm
bu fc
2 F /|______Helvetica fnt
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(N)show
236 428 gm
9 fz
bu fc
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(21)show
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0 gr
171.5 361.5 241.5 503.5 0 rc
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224 389 gm
237 402 lin
237 388 gm
224 401 lin
224 420 gm
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237 419 gm
224 432 lin
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203 403 lin
203 389 gm
190 402 lin
174 389 gm
187 402 lin
187 388 gm
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219 432 lin
219 419 gm
207 432 lin
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219 402 lin
219 388 gm
207 401 lin
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182 174 gm
(nc 172 173 184 195 6 rc)kp
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2 F /|______Geneva fnt
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338 275 364 301 0 ov
1 1 pen
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0 0 2 9 12 2 dh
340 351 lin
rh
psb
pse
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0 0 2 9 5 2 dh
1 1 pen
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rh
psb
pse
282 318 lin
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222 182 lin
191 183 gm
223 286 lin
0 0 2 9 5 2 dh
232 99 gm
191 182 lin
rh
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pse
353 281 gm
(nc 345 280 356 296 6 rc)kp
F 1 setTxMode
bu fc
2 F /|______Helvetica fnt
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(N)show
7 fz
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(41)show
296 312 gm
(nc 288 311 299 328 6 rc)kp
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(N)show
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(36)show
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(nc 230 175 241 191 6 rc)kp
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(N)show
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(22)show
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(nc 229 280 240 296 6 rc)kp
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(N)show
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(23)show
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(nc 173 199 184 210 6 rc)kp
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(P)show
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(1)show
238 302 gm
(nc 230 301 241 313 6 rc)kp
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(P)show
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(2)show
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(nc 287 333 298 345 6 rc)kp
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(P)show
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(3)show
238 199 gm
(nc 230 198 241 210 6 rc)kp
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(P)show
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(1)show
355 304 gm
(nc 347 303 358 315 6 rc)kp
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(P)show
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(2)show
(nc 164 97 366 505 6 rc)kp
0 gr
280.5 202.5 306.5 228.5 0 ov
0 0 2 9 5 2 dh
279 151 gm
248 182 lin
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280 215 lin
295 209 gm
(nc 287 208 298 225 6 rc)kp
F 1 setTxMode
9 fz
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2 F /|______Helvetica fnt
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(N)show
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(34)show
296 231 gm
(nc 288 230 299 241 6 rc)kp
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(P)show
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(2)show
153 77 gm
(nc 30 28 811 566 6 rc)kp
0 gr
153 525 lin
394 202 gm
F 1 setTxMode
11 fz
bu fc
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(Fig.3 )show
1 fs
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(Snapshot of a splitting during search)show
412 77 gm
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412 525 lin
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F 1 setTxMode
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1.40029 0. 32 0.14002 0.(In Fig.3 process P)awidthshow
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0.38081 0.(4)ashow
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1.14730 0. 32 0.11473 0.( is idle because it has completed its own list of tasks; P)awidthshow
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0.38081 0.(1)ashow
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1.08932 0. 32 0.10893 0.( is waiting for N)awidthshow
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(34)show
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0.39398 0. 32 0.03939 0.(minimax value from process P)awidthshow
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0.12751 0.(2)ashow
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0.46432 0. 32 0.04643 0.(; likewise, P)awidthshow
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0.12751 0.(3)ashow
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0.35842 0. 32 0.03584 0.( is waiting for N)awidthshow
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0.12751 0.(41)ashow
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0.40191 0. 32 0.04019 0.( value from P)awidthshow
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0.12092 0.(2)ashow
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0.47790 0. 32 0.04779 0.(. Therefore, P)awidthshow
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0.12092 0.(2)ashow
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0.27145 0. 32 0.02714 0.( is the)awidthshow
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0.43975 0. 32 0.04397 0.(only process working at present: it is evaluating N)awidthshow
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0.11721 0.(41)ashow
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0.42282 0. 32 0.04228 0.(. There is a hierarchic relation between P)awidthshow
453 499 gm
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0.13636 0.(3)ashow
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0.43426 0. 32 0.04342 0.( and)awidthshow
464 79 gm
(P)show
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(2)show
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(: it will be reversed when, having completed N)show
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(36)show
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( evaluation, P)show
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( sends a message to P)show
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(2)show
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( .)show
475 79 gm
0.93658 0. 32 0.09365 0.(The main problem in searching a game tree by a splitting method is to decide when the subtree)awidthshow
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(-)show
486 79 gm
1.91757 0. 32 0.19175 0.(process association should be established. Usually, it makes no sense to allocate subtrees to)awidthshow
497 79 gm
(processes before search starts, because of the following reasons:)show
509 88 gm
(\245 it is necessary to know the whole tree;)show
526 88 gm
1.29272 0. 32 0.12927 0.(\245 the\312)awidthshow
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0.45089 0. 32 0.04508 0.( the identity of these subtrees and then to obtain at run-time a)awidthshow
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(uniform load distribution.)show
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1.13494 0. 32 0.11349 0.(At search time we usually have the following scenery: some "lucky" processes complete search)awidthshow
572 79 gm
0.15518 0. 32 0.01551 0.(before others \()awidthshow
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1.27334 0. 32 0.12733 0.(must be dynamic, )awidthshow
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0.33239 0.(i.e.)ashow
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1.44989 0. 32 0.14498 0.(, it must provide mechanisms able, during the search, to reassign to idle)awidthshow
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0.41198 0. 32 0.04119 0.(processes subtrees already assigned to overloaded processes. Therefore, a classification of splitting)awidthshow
605 79 gm
0.27206 0. 32 0.02720 0.(methods in static and dynamic is not really meaningful, because actually the only plausible solution)awidthshow
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(Def)show
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0.72387 0. 32 0.07238 0.(: Let D be a splitting for game tree A; let N)awidthshow
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0.00639 0.(splitting)ashow
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(node)show
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( \(according to D\) )show
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(\333 $)show
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(N)show
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(j)show
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(: N)show
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(i)show
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(=father\(N)show
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(\) and D\(N)show
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(\))show
currentfont SwToSym
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(D\(N)show
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(i)show
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(\).)show
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0.38619 0. 32 0.03861 0.(A splitting node is one at which it is established the generation of a parallel search task, )awidthshow
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0.11729 0.(i.e.)ashow
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0.39413 0. 32 0.03941 0.(, where)awidthshow
678 79 gm
1.34124 0. 32 0.13412 0.(some of its subtrees are visited by processes different from its explorer. We can now state the)awidthshow
689 79 gm
(following classification:)show
701 88 gm
(\245 a )show
701 102 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
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(static)show
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0 fs
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2 F /|______Times-Roman fnt
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( splitting algorithm decides all the splitting nodes before the search starts;)show
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(\245 a )show
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2 F /|______Times-Italic fnt
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(dynamic)show
714 139 gm
0 fs
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( algorithm decides some splitting nodes only during the search.)show
745 79 gm
1 fs
12 fz
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(3. Parallel search on a network of workstations)show
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op
30 28 811 566 fr
0 0 xl
1 1 pen
0 0 gm
(nc 0 0 0 0 6 rc)kp
91 336 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0 fs
10 fz
bu fc
2 F /|______Helvetica fnt
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(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
773 519 gm
(5)show
118 79 gm
11 fz
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2 F /|______Times-Roman fnt
bn
0.48721 0. 32 0.04872 0.(High-level parallel programming languages are gaining momentum, because they simplify the task)awidthshow
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0.53451 0. 32 0.05345 0.(of building software for the novel architectures with several processors. Parallel search algorithms)awidthshow
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(are good tests for these new languages.)show
151 79 gm
0.06134 0. 32 0.00613 0.(Parallel search algorithms have been programmed in several languages; for instance, in [ABD82] we)awidthshow
162 79 gm
0.90576 0. 32 0.09057 0.(find an algorithm based on semaphore primitives; in [Eli90] the Orca language was used. In this)awidthshow
173 79 gm
2.62359 0. 32 0.26235 0.(paper we will use Linda, a coordination language that consists of a small set of parallel)awidthshow
184 79 gm
0.30395 0. 32 0.03039 0.(programming primitives that can be added to any sequential language [CarGel90]. These primitives)awidthshow
195 79 gm
(associatively access a )show
195 177 gm
2 fs
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(tuple space)show
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( shared among processes.)show
206 79 gm
0.74050 0. 32 0.07405 0.(There are several possible software architectures that can all be programmed in Linda; one of the)awidthshow
217 79 gm
0.73242 0. 32 0.07324 0.(most useful is the )awidthshow
217 163 gm
2 fs
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0.15429 0.(master-worker)ashow
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2 F /|______Times-Roman fnt
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0.53817 0. 32 0.05381 0.( model. According to this model tasks created during the parallel)awidthshow
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0.18966 0. 32 0.01896 0.(evaluation of a program are dynamically distributed among processors. The parallel program should)awidthshow
239 79 gm
(be structured as follows:)show
251 88 gm
(\245 a )show
251 102 gm
2 fs
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(master)show
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( process generates tasks and coordinates the collection of solutions;)show
264 88 gm
0.61599 0. 32 0.06159 0.(\245 several identical )awidthshow
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2 fs
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(worker)show
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2 F /|______Times-Roman fnt
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0.63095 0. 32 0.06309 0.( processes pick and execute tasks and return task results to the master;)awidthshow
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(when a task is terminated, a new task can be chosen;)show
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0.14007 0. 32 0.01400 0.(\245 in the tuple space there are two main kinds of tuples: active tuples for tasks \(we call this multiset)awidthshow
299 101 gm
(the agenda\), and passive tuples that represent task results.)show
311 79 gm
1.13449 0. 32 0.11344 0.(The master)awidthshow
311 130 gm
1.33850 0. 32 0.13385 0.(-worker model allows to structure the supervisor of a node as a master process that)awidthshow
322 79 gm
0.12695 0. 32 0.01269 0.(coordinates several explorers as workers. This is simple to model: in the following program only the)awidthshow
333 79 gm
(root is a splitting node.)show
340 78 gm
(nc 336 79 348 525 6 rc)kp
0 gr
340 525 lin
368 97 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
10 fz
bu fc
2 F /|______Courier fnt
bn
(int\312master_main\(int\312n_worker,int\312depth\))show
379 97 gm
({)show
390 97 gm
(position\312*root,*successor;)show
401 97 gm
(int\312nmoves,minimax,i,master\(\),worker\(\);)show
412 97 gm
(for \(i=0;i<n_worker;i++\))show
423 115 gm
(eval \("worker",worker\(depth\)\);  /* create n workers */)show
434 97 gm
(while \(!end\(\)\))show
445 115 gm
({)show
456 115 gm
(load_new_position \(&root\); /* a new game tree */)show
467 115 gm
(nmoves=genmoves\(root,&successor\);)show
478 115 gm
(if \(nmoves==0\)   /* no search to do? */)show
489 133 gm
(return\(evaluate\(root\)\);)show
500 115 gm
(out \("root",*root\); /* put new tree in agenda */)show
511 115 gm
(out\312\("sync",n_worker\);)show
522 115 gm
(for \(i=0;i<n_worker;i++\))show
533 133 gm
(out\312\("job",NEW_POSITION\); /* new job */)show
544 115 gm
0.42297 0. 32 0.04229 0.(in\312\("sync",0\); /* master continues only after all workers are ready)awidthshow
555 97 gm
(*/)show
566 115 gm
(minimax=master\(n_worker,nmoves,depth,successor\);/* search */)show
577 115 gm
(in\312\("root",*root\);  /* delete visited tree */)show
588 115 gm
(})show
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(for \(i=0;i<n_worker;i++\))show
610 115 gm
({)show
621 115 gm
(out\("job",QUIT\);  /* end of task */)show
632 115 gm
(in\("worker", 0\);  /* delete worker */)show
643 115 gm
(})show
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(return \(0\);)show
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(})show
687 97 gm
(int\312master\(int\312n_worker,int\312nmoves\))show
698 97 gm
({)show
709 97 gm
(int\312nmoves,local_score,subtree,free,best;)show
720 97 gm
(local_score=-INFINITE;  /* initialize local score */)show
731 97 gm
(out\312\("score", local_score\);  /* initialize global score */)show
742 97 gm
(free = n_worker;)show
753 97 gm
(subtree = 1;)show
F T cp
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0 0 xl
1 1 pen
0 0 gm
(nc 0 0 0 0 6 rc)kp
91 336 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0 fs
10 fz
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(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
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(6)show
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bu fc
2 F /|______Courier fnt
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(while \(\(subtree <= nmoves\) || \(free<n_worker\)\))show
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(/* loop terminates when job done */)show
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(if \(\(subtree <= nmoves\) && \(free>0\)\))show
152 169 gm
(/* more tasks in agenda and a worker is idle? */)show
163 133 gm
({ out\("job",subtree\); /* insert search task in agenda */)show
174 133 gm
(free--;)show
185 133 gm
(subtree++;)show
196 133 gm
(})show
207 115 gm
(else     /* wait completion of a task */)show
218 133 gm
({)show
229 133 gm
(in \("result",?value,?r_subtree\);  /* get result */)show
240 133 gm
(if \(value>local_score\)  /* improved score? */)show
251 151 gm
({ local_score=value;     /* local update of score */)show
262 151 gm
(in \("score",?int\);)show
273 151 gm
(out\("score",local_score\); /* global update of score */)show
284 151 gm
(best=r_subtree;)show
295 151 gm
(})show
306 133 gm
(free++;})show
317 97 gm
(in \("score",?int\); /* to avoid interference with next search */)show
329 97 gm
(return \(local_score\);)show
340 97 gm
(})show
360 233 gm
11 fz
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(Fig)show
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(.)show
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(4)show
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( Core algorithm: master)show
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0 gr
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397 79 gm
F 1 setTxMode
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0.75927 0. 32 0.07592 0.(Creating and terminating an active tuple for each task is an expensive activity in Network Linda,)awidthshow
408 79 gm
1.31683 0. 32 0.13168 0.(thus we have defined a general worker structure that can survive the end of a task and can be)awidthshow
419 79 gm
(specialized when it is necessary.)show
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(nc 422 79 434 525 6 rc)kp
0 gr
426 525 lin
455 97 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
10 fz
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2 F /|______Courier fnt
bn
(int\312worker\(int depth\))show
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({)show
479 97 gm
(position *root,*successor,*tree_pointer;)show
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(int nmoves,subtree,score,value,job_type,quit,s;)show
503 97 gm
(quit=false;)show
515 97 gm
(while\(!quit\))show
527 115 gm
({)show
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(in\("job",?job_type\);)show
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(switch\312\(job_type\))show
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({)show
575 133 gm
(case\312QUIT:  /* terminate */)show
587 151 gm
(quit=true;)show
599 151 gm
(break;)show
611 133 gm
(case\312NEW_POSITION: /* new game tree */)show
623 151 gm
(in\("position",?*root\);)show
635 151 gm
(in\("sync",?s\);)show
647 151 gm
(out\("sync",s-1\);)show
659 151 gm
(nmoves=genmoves\(root,&successor\);)show
671 151 gm
(break;)show
683 133 gm
(default: /* sequential )show
bu fc
2 F /|______Symbol fnt
bn
(ab)show
bu fc
2 F /|______Courier fnt
bn
( */)show
695 151 gm
(subtree=job_type;)show
707 151 gm
(tree_pointer=successor+subtree-1;)show
719 151 gm
(makemove\(tree_pointer\);)show
731 151 gm
(rd\("score",?score\);  /* update local score */)show
743 151 gm
(value=-alphabeta\(tree_pointer,-INFINITE,-score,depth\);)show
F T cp
%%Page: ? 9
op
30 28 811 566 fr
0 0 xl
1 1 pen
0 0 gm
(nc 0 0 0 0 6 rc)kp
91 336 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0 fs
10 fz
bu fc
2 F /|______Helvetica fnt
bn
(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
773 519 gm
(7)show
119 151 gm
bu fc
2 F /|______Courier fnt
bn
(out\("result",value,subtree\);)show
131 151 gm
(undomove\(tree_pointer\);)show
143 151 gm
(break;)show
155 133 gm
(})show
167 115 gm
(})show
179 97 gm
(return\312\(0\);})show
199 232 gm
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
(Fig)show
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(.)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(5)show
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
( Core algorithm: worker)show
217 77 gm
0 gr
217 525 lin
236 79 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
1.33102 0. 32 0.13310 0.(Our goal is to compare some parallel search strategies with their sequential versions. We have)awidthshow
247 79 gm
1.65176 0. 32 0.16517 0.(developed and tested different programs all based on such an algorithm. The experiments we)awidthshow
258 79 gm
1.15219 0. 32 0.11521 0.(describe used the Bratko)awidthshow
258 193 gm
1.17324 0. 32 0.11732 0.(-Kopec positions [BraKop82] to measure the speedup on an increasing)awidthshow
269 79 gm
(number of workstations.)show
280 79 gm
0.13885 0. 32 0.01388 0.(The most important value we measured is time T to search a game tree. For sequential versions, this)awidthshow
295 79 gm
0.11901 0. 32 0.01190 0.(is defined as the interval between the root invocation of )awidthshow
295 328 gm
bu fc
2 F /|______Symbol fnt
bn
0.03961 0.(ab)ashow
bu fc
2 F /|______Times-Roman fnt
bn
0.11077 0. 32 0.01107 0.( and its termination \(we actually measure)awidthshow
307 79 gm
0.33569 0. 32 0.03356 0.(CPU time used for such an evaluation\). For the parallel versions, we let the master to measure time)awidthshow
318 79 gm
1.42822 0. 32 0.14282 0.(between the distribution of the root node and the collection of its minimax value \(for such an)awidthshow
329 79 gm
0.63201 0. 32 0.06320 0.(evaluation we used real time; the network was used during unloaded hours\). Other parameters we)awidthshow
340 79 gm
(recorded are shown in Fig.6.)show
369 110 gm
1 fs
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(Procs)show
369 167 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(processors used for the search \(master+workers\))show
355 80 gm
0 gr
355 82 lin
355 80 gm
357 80 lin
357 82 gm
357 82 lin
357 82 lin
355 83 gm
355 161 lin
357 83 gm
357 161 lin
355 162 gm
355 164 lin
357 162 gm
357 164 lin
355 165 gm
355 468 lin
357 165 gm
357 468 lin
355 469 gm
355 471 lin
357 471 lin
357 469 gm
357 469 lin
357 469 lin
358 80 gm
371 80 lin
358 82 gm
371 82 lin
358 162 gm
371 162 lin
358 469 gm
371 469 lin
358 471 gm
371 471 lin
390 119 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(T)show
386 167 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(total search time in seconds for all 24 positions)show
372 82 gm
0 gr
374 82 lin
372 80 gm
374 80 lin
372 83 gm
372 161 lin
374 83 gm
374 161 lin
372 162 gm
372 164 lin
374 162 gm
374 164 lin
372 165 gm
372 468 lin
374 165 gm
374 468 lin
372 471 gm
374 471 lin
372 469 gm
374 469 lin
375 80 gm
392 80 lin
375 82 gm
392 82 lin
375 162 gm
392 162 lin
375 469 gm
392 469 lin
375 471 gm
392 471 lin
411 119 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(N)show
407 167 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(total searched nodes for all 24 positions)show
393 82 gm
0 gr
395 82 lin
393 80 gm
395 80 lin
393 83 gm
393 161 lin
395 83 gm
395 161 lin
393 162 gm
393 164 lin
395 162 gm
395 164 lin
393 165 gm
393 468 lin
395 165 gm
395 468 lin
393 471 gm
395 471 lin
393 469 gm
395 469 lin
396 80 gm
413 80 lin
396 82 gm
413 82 lin
396 162 gm
413 162 lin
396 469 gm
413 469 lin
396 471 gm
413 471 lin
437 119 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(S)show
434 167 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(speedup )show
0 0 pen
445 254 gm
(nc 419 202 445 254 6 rc)kp
0 gr
445 254 lin
psb
currentpoint
pse
419 202 gm
419 202 lin
psb
30 dict begin
currentpoint 3 -1 roll sub neg 3 1 roll sub 1664 div 832 3 -1 roll exch div scale currentpoint translate 64 46 translate
-23 434 moveto
/fs 0 def
/sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def
/f1 {findfont dup /cf exch def sf} def
/ns {cf sf} def
320 /Helvetica f1
(\() show
99 434 moveto
320 /Symbol f1
(=) show
760 233 moveto
320 /Helvetica f1
(T) show
955 233 moveto
256 /Helvetica f1
(1) show
392 679 moveto
320 /Helvetica f1
(T) show
587 679 moveto
256 ns
(nr) show
821 679 moveto
256 /Helvetica f1
(.) show
920 679 moveto
256 /Helvetica f1
(proc) show
/thick 0 def
/th { dup setlinewidth /thick exch def } def
16 th 366 351 moveto 1077 0 rlineto stroke
1463 434 moveto
320 /Helvetica f1
(\)) show
end
pse
1 1 pen
414 82 gm
(nc 30 28 811 566 6 rc)kp
416 82 lin
414 80 gm
416 80 lin
414 83 gm
414 161 lin
416 83 gm
416 161 lin
414 162 gm
414 164 lin
416 162 gm
416 164 lin
414 165 gm
414 468 lin
416 165 gm
416 468 lin
414 471 gm
416 471 lin
414 469 gm
416 469 lin
417 80 gm
445 80 lin
417 82 gm
445 82 lin
417 162 gm
445 162 lin
417 469 gm
445 469 lin
417 471 gm
445 471 lin
469 119 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(E)show
466 167 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(relative efficiency  )show
0 0 pen
477 295 gm
(nc 451 244 477 295 6 rc)kp
0 gr
477 295 lin
psb
currentpoint
pse
451 244 gm
451 244 lin
psb
30 dict begin
currentpoint 3 -1 roll sub neg 3 1 roll sub 1632 div 832 3 -1 roll exch div scale currentpoint translate 64 42 translate
-23 438 moveto
/fs 0 def
/sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def
/f1 {findfont dup /cf exch def sf} def
/ns {cf sf} def
320 /Helvetica f1
(\() show
99 438 moveto
320 /Symbol f1
(=) show
783 237 moveto
320 /Helvetica f1
(S) show
376 683 moveto
(nr) show
660 683 moveto
320 /Helvetica f1
(.) show
768 683 moveto
320 /Helvetica f1
(proc) show
/thick 0 def
/th { dup setlinewidth /thick exch def } def
16 th 366 355 moveto 1046 0 rlineto stroke
1432 438 moveto
320 /Helvetica f1
(\)) show
end
pse
1 1 pen
446 82 gm
(nc 30 28 811 566 6 rc)kp
448 82 lin
446 80 gm
448 80 lin
446 83 gm
446 161 lin
448 83 gm
448 161 lin
446 162 gm
446 164 lin
448 162 gm
448 164 lin
446 165 gm
446 468 lin
448 165 gm
448 468 lin
446 471 gm
448 471 lin
446 469 gm
448 469 lin
449 80 gm
477 80 lin
449 82 gm
477 82 lin
449 162 gm
477 162 lin
449 469 gm
477 469 lin
449 471 gm
477 471 lin
492 112 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fpm)show
492 167 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(average production factor)show
478 82 gm
0 gr
480 82 lin
478 80 gm
480 80 lin
478 83 gm
478 161 lin
480 83 gm
480 161 lin
478 162 gm
478 164 lin
480 162 gm
480 164 lin
478 165 gm
478 468 lin
480 165 gm
480 468 lin
478 471 gm
480 471 lin
478 469 gm
480 469 lin
481 80 gm
494 80 lin
481 82 gm
494 82 lin
481 162 gm
494 162 lin
481 469 gm
494 469 lin
481 471 gm
494 471 lin
509 109 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fpmw)show
509 167 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(average production factor for workers)show
495 82 gm
0 gr
497 82 lin
495 80 gm
497 80 lin
495 83 gm
495 161 lin
497 83 gm
497 161 lin
495 162 gm
495 164 lin
497 162 gm
497 164 lin
495 165 gm
495 468 lin
497 165 gm
497 468 lin
495 471 gm
497 471 lin
495 469 gm
497 469 lin
498 80 gm
511 80 lin
498 82 gm
511 82 lin
498 162 gm
511 162 lin
498 469 gm
511 469 lin
498 471 gm
511 471 lin
535 116 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(SO)show
532 167 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(search overhead )show
0 0 pen
541 299 gm
(nc 517 234 541 299 6 rc)kp
0 gr
541 299 lin
psb
currentpoint
pse
517 234 gm
517 234 lin
psb
30 dict begin
currentpoint 3 -1 roll sub neg 3 1 roll sub 2080 div 768 3 -1 roll exch div scale currentpoint translate 64 46 translate
-23 434 moveto
/fs 0 def
/sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def
/f1 {findfont dup /cf exch def sf} def
/ns {cf sf} def
320 /Helvetica f1
(\() show
99 434 moveto
320 /Symbol f1
(=) show
374 233 moveto
320 /Helvetica f1
(N) show
605 233 moveto
256 ns
(nr) show
839 233 moveto
256 /Helvetica f1
(.) show
938 233 moveto
256 /Helvetica f1
(proc) show
751 679 moveto
320 ns
(N) show
963 679 moveto
256 /Helvetica f1
(1) show
/thick 0 def
/th { dup setlinewidth /thick exch def } def
16 th 366 351 moveto 1095 0 rlineto stroke
1538 434 moveto
320 /Symbol f1
(-) show
1757 434 moveto
320 /Helvetica f1
(1) show
1888 434 moveto
320 /Helvetica f1
(\)) show
end
pse
1 1 pen
512 82 gm
(nc 30 28 811 566 6 rc)kp
514 82 lin
512 80 gm
514 80 lin
512 83 gm
512 161 lin
514 83 gm
514 161 lin
512 162 gm
512 164 lin
514 162 gm
514 164 lin
512 165 gm
512 468 lin
514 165 gm
514 468 lin
512 471 gm
514 471 lin
512 469 gm
514 469 lin
515 80 gm
541 80 lin
515 82 gm
541 82 lin
515 162 gm
541 162 lin
515 469 gm
541 469 lin
515 471 gm
541 471 lin
565 117 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(SS)show
562 167 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(search speed )show
0 0 pen
571 246 gm
(nc 547 220 571 246 6 rc)kp
0 gr
571 246 lin
psb
currentpoint
pse
547 220 gm
547 220 lin
psb
30 dict begin
currentpoint 3 -1 roll sub neg 3 1 roll sub 832 div 768 3 -1 roll exch div scale currentpoint translate 64 46 translate
-23 434 moveto
/fs 0 def
/sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def
/f1 {findfont dup /cf exch def sf} def
/ns {cf sf} def
320 /Helvetica f1
(\() show
99 434 moveto
320 /Symbol f1
(=) show
374 233 moveto
320 /Helvetica f1
(N) show
392 679 moveto
(T) show
/thick 0 def
/th { dup setlinewidth /thick exch def } def
16 th 366 351 moveto 247 0 rlineto stroke
633 434 moveto
320 /Helvetica f1
(\)) show
end
pse
1 1 pen
542 82 gm
(nc 30 28 811 566 6 rc)kp
544 82 lin
542 80 gm
544 80 lin
542 83 gm
542 161 lin
544 83 gm
544 161 lin
542 162 gm
542 164 lin
544 162 gm
544 164 lin
542 165 gm
542 468 lin
544 165 gm
544 468 lin
542 471 gm
544 471 lin
542 469 gm
544 469 lin
545 80 gm
571 80 lin
545 82 gm
571 82 lin
545 162 gm
571 162 lin
545 469 gm
571 469 lin
545 471 gm
571 471 lin
595 114 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(S)show
9 fz
bu fc
2 F /|______Times-Bold fnt
bn
(SS)show
592 167 gm
0 fs
10 fz
bu fc
2 F /|______Times-Roman fnt
bn
(speed gain )show
0 0 pen
601 271 gm
(nc 577 211 601 271 6 rc)kp
0 gr
601 271 lin
psb
currentpoint
pse
577 211 gm
577 211 lin
psb
30 dict begin
currentpoint 3 -1 roll sub neg 3 1 roll sub 1920 div 768 3 -1 roll exch div scale currentpoint translate 64 46 translate
-23 434 moveto
/fs 0 def
/sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def
/f1 {findfont dup /cf exch def sf} def
/ns {cf sf} def
320 /Helvetica f1
(\() show
99 434 moveto
320 /Symbol f1
(=) show
389 233 moveto
320 /Helvetica f1
(VR) show
866 233 moveto
256 ns
(nr) show
1100 233 moveto
256 /Helvetica f1
(.) show
1199 233 moveto
256 /Helvetica f1
(proc) show
778 679 moveto
320 ns
(VR) show
1214 679 moveto
256 /Helvetica f1
(1) show
/thick 0 def
/th { dup setlinewidth /thick exch def } def
16 th 366 351 moveto 1356 0 rlineto stroke
1742 434 moveto
320 /Helvetica f1
(\)) show
end
pse
1 1 pen
572 82 gm
(nc 30 28 811 566 6 rc)kp
574 82 lin
572 80 gm
574 80 lin
572 83 gm
572 161 lin
574 83 gm
574 161 lin
572 162 gm
572 164 lin
574 162 gm
574 164 lin
572 165 gm
572 468 lin
574 165 gm
574 468 lin
572 471 gm
574 471 lin
572 469 gm
574 469 lin
575 80 gm
601 80 lin
575 82 gm
601 82 lin
604 80 gm
604 82 lin
602 80 gm
604 80 lin
602 82 gm
602 82 lin
602 82 lin
602 83 gm
602 161 lin
604 83 gm
604 161 lin
575 162 gm
601 162 lin
602 162 gm
602 164 lin
604 162 gm
604 164 lin
602 165 gm
602 468 lin
604 165 gm
604 468 lin
575 469 gm
601 469 lin
575 471 gm
601 471 lin
604 469 gm
604 471 lin
602 471 gm
604 471 lin
602 469 gm
602 469 lin
602 469 lin
616 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig 6)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Parameters we measured in the experiments)show
632 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.66162 0. 32 0.06616 0.(All experiments were done fixing a search depth of 5 plies, for comparison with other papers that)awidthshow
643 79 gm
0.46813 0. 32 0.04681 0.(used the same search depth. We have used 11 Sun Sparcstations in periods when they were free of)awidthshow
654 79 gm
(other tasks.)show
684 79 gm
1 fs
12 fz
bu fc
2 F /|______Times-Bold fnt
bn
(4. Static splitting)show
697 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.44723 0. 32 0.04472 0.(Let us discuss preliminarly a few results we can expect from our experiments. Let B the branching)awidthshow
708 79 gm
(factor typical of chess game trees, and N)show
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(w )show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
(the number of processors available for explorers:)show
720 88 gm
(\245\312the core algorithm efficiency should be proportional to the ratio B/N)show
720 396 gm
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(w)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
( [MarCam82];)show
737 88 gm
0.22293 0. 32 0.02229 0.(\245\312for a game tree with B=40, an )awidthshow
bu fc
2 F /|______Symbol fnt
bn
0.10455 0.(ab)ashow
bu fc
2 F /|______Times-Roman fnt
bn
0.24337 0. 32 0.02433 0.( search is equivalent to a minimax search of a tree with branch)awidthshow
749 101 gm
(factor B=7 [Gil72]. Thus, if we had N)show
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(w)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
(=40 explorers, the ideal average speedup should be 7.)show
F T cp
%%Page: ? 10
op
30 28 811 566 fr
0 0 xl
1 1 pen
0 0 gm
(nc 0 0 0 0 6 rc)kp
91 336 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0 fs
10 fz
bu fc
2 F /|______Helvetica fnt
bn
(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
773 519 gm
(8)show
136 96 gm
1 fs
9 fz
bu fc
2 F /|______Times-Bold fnt
bn
(Procs)show
136 141 gm
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(T\(sec\))show
136 188 gm
9 fz
bu fc
2 F /|______Times-Bold fnt
bn
(N \(nodes\))show
136 249 gm
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(S)show
136 282 gm
(E)show
136 310 gm
(Fpm)show
136 344 gm
9 fz
bu fc
2 F /|______Times-Bold fnt
bn
(Fpmw)show
136 385 gm
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(SO)show
136 425 gm
9 fz
bu fc
2 F /|______Times-Bold fnt
bn
(SS \(nodes/sec\))show
136 505 gm
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(Sss)show
122 80 gm
0 gr
122 82 lin
122 80 gm
124 80 lin
124 82 gm
124 82 lin
124 82 lin
122 83 gm
122 128 lin
124 83 gm
124 128 lin
122 129 gm
122 131 lin
124 129 gm
124 131 lin
122 132 gm
122 175 lin
124 132 gm
124 175 lin
122 176 gm
122 178 lin
124 176 gm
124 178 lin
122 179 gm
122 232 lin
124 179 gm
124 232 lin
122 233 gm
122 235 lin
124 233 gm
124 235 lin
122 236 gm
122 266 lin
124 236 gm
124 266 lin
122 267 gm
122 269 lin
124 267 gm
124 269 lin
122 270 gm
122 300 lin
124 270 gm
124 300 lin
122 301 gm
122 303 lin
124 301 gm
124 303 lin
122 304 gm
122 334 lin
124 304 gm
124 334 lin
122 335 gm
122 337 lin
124 335 gm
124 337 lin
122 338 gm
122 372 lin
124 338 gm
124 372 lin
122 373 gm
122 375 lin
124 373 gm
124 375 lin
122 376 gm
122 406 lin
124 376 gm
124 406 lin
122 407 gm
122 409 lin
124 407 gm
124 409 lin
122 410 gm
122 492 lin
124 410 gm
124 492 lin
122 493 gm
122 495 lin
124 493 gm
124 495 lin
122 496 gm
122 526 lin
124 496 gm
124 526 lin
122 527 gm
122 529 lin
124 529 lin
124 527 gm
124 527 lin
124 527 lin
125 80 gm
138 80 lin
125 82 gm
138 82 lin
125 129 gm
138 129 lin
125 131 gm
138 131 lin
125 176 gm
138 176 lin
125 178 gm
138 178 lin
125 233 gm
138 233 lin
125 235 gm
138 235 lin
125 267 gm
138 267 lin
125 269 gm
138 269 lin
125 301 gm
138 301 lin
125 303 gm
138 303 lin
125 335 gm
138 335 lin
125 337 gm
138 337 lin
125 373 gm
138 373 lin
125 375 gm
138 375 lin
125 407 gm
138 407 lin
125 409 gm
138 409 lin
125 493 gm
138 493 lin
125 495 gm
138 495 lin
125 527 gm
138 527 lin
125 529 gm
138 529 lin
153 104 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
153 144 gm
(8301)show
153 189 gm
(5347545)show
153 247 gm
(---)show
153 281 gm
(---)show
153 315 gm
(---)show
153 351 gm
(---)show
153 387 gm
(---)show
153 444 gm
(644)show
153 507 gm
(---)show
139 82 gm
0 gr
141 82 lin
139 80 gm
141 80 lin
139 83 gm
139 128 lin
141 83 gm
141 128 lin
139 131 gm
139 131 lin
141 129 gm
141 129 lin
139 129 gm
139 129 lin
141 131 gm
141 131 lin
139 132 gm
139 175 lin
141 132 gm
141 175 lin
139 178 gm
139 178 lin
141 176 gm
141 176 lin
139 176 gm
139 176 lin
141 178 gm
141 178 lin
139 179 gm
139 232 lin
141 179 gm
141 232 lin
139 235 gm
139 235 lin
141 233 gm
141 233 lin
139 233 gm
139 233 lin
141 235 gm
141 235 lin
139 236 gm
139 266 lin
141 236 gm
141 266 lin
139 269 gm
139 269 lin
141 267 gm
141 267 lin
139 267 gm
139 267 lin
141 269 gm
141 269 lin
139 270 gm
139 300 lin
141 270 gm
141 300 lin
139 303 gm
139 303 lin
141 301 gm
141 301 lin
139 301 gm
139 301 lin
141 303 gm
141 303 lin
139 304 gm
139 334 lin
141 304 gm
141 334 lin
139 337 gm
139 337 lin
141 335 gm
141 335 lin
139 335 gm
139 335 lin
141 337 gm
141 337 lin
139 338 gm
139 372 lin
141 338 gm
141 372 lin
139 375 gm
139 375 lin
141 373 gm
141 373 lin
139 373 gm
139 373 lin
141 375 gm
141 375 lin
139 376 gm
139 406 lin
141 376 gm
141 406 lin
139 409 gm
139 409 lin
141 407 gm
141 407 lin
139 407 gm
139 407 lin
141 409 gm
141 409 lin
139 410 gm
139 492 lin
141 410 gm
141 492 lin
139 495 gm
139 495 lin
141 493 gm
141 493 lin
139 493 gm
139 493 lin
141 495 gm
141 495 lin
139 496 gm
139 526 lin
141 496 gm
141 526 lin
139 529 gm
141 529 lin
139 527 gm
141 527 lin
142 80 gm
155 80 lin
142 82 gm
155 82 lin
142 129 gm
155 129 lin
142 131 gm
155 131 lin
142 176 gm
155 176 lin
142 178 gm
155 178 lin
142 233 gm
155 233 lin
142 235 gm
155 235 lin
142 267 gm
155 267 lin
142 269 gm
155 269 lin
142 301 gm
155 301 lin
142 303 gm
155 303 lin
142 335 gm
155 335 lin
142 337 gm
155 337 lin
142 373 gm
155 373 lin
142 375 gm
155 375 lin
142 407 gm
155 407 lin
142 409 gm
155 409 lin
142 493 gm
155 493 lin
142 495 gm
155 495 lin
142 527 gm
155 527 lin
142 529 gm
155 529 lin
168 104 gm
F 1 setTxMode
(3)show
168 144 gm
(4571)show
168 189 gm
(5754203)show
168 243 gm
(1.82)show
168 277 gm
(0.61)show
168 311 gm
(0.66)show
168 347 gm
(0.98)show
168 383 gm
(0.08)show
168 442 gm
(1259)show
168 503 gm
(1.95)show
156 82 gm
0 gr
156 82 lin
156 80 gm
156 80 lin
156 83 gm
156 128 lin
156 131 gm
156 131 lin
156 129 gm
156 129 lin
156 132 gm
156 175 lin
156 178 gm
156 178 lin
156 176 gm
156 176 lin
156 179 gm
156 232 lin
156 235 gm
156 235 lin
156 233 gm
156 233 lin
156 236 gm
156 266 lin
156 269 gm
156 269 lin
156 267 gm
156 267 lin
156 270 gm
156 300 lin
156 303 gm
156 303 lin
156 301 gm
156 301 lin
156 304 gm
156 334 lin
156 337 gm
156 337 lin
156 335 gm
156 335 lin
156 338 gm
156 372 lin
156 375 gm
156 375 lin
156 373 gm
156 373 lin
156 376 gm
156 406 lin
156 409 gm
156 409 lin
156 407 gm
156 407 lin
156 410 gm
156 492 lin
156 495 gm
156 495 lin
156 493 gm
156 493 lin
156 496 gm
156 526 lin
156 529 gm
156 529 lin
156 527 gm
156 527 lin
157 80 gm
170 80 lin
157 82 gm
170 82 lin
157 129 gm
170 129 lin
157 131 gm
170 131 lin
157 176 gm
170 176 lin
157 178 gm
170 178 lin
157 233 gm
170 233 lin
157 235 gm
170 235 lin
157 267 gm
170 267 lin
157 269 gm
170 269 lin
157 301 gm
170 301 lin
157 303 gm
170 303 lin
157 335 gm
170 335 lin
157 337 gm
170 337 lin
157 373 gm
170 373 lin
157 375 gm
170 375 lin
157 407 gm
170 407 lin
157 409 gm
170 409 lin
157 493 gm
170 493 lin
157 495 gm
170 495 lin
157 527 gm
170 527 lin
157 529 gm
170 529 lin
183 104 gm
F 1 setTxMode
(5)show
183 144 gm
(2770)show
183 189 gm
(6599460)show
183 243 gm
(3.00)show
183 277 gm
(0.60)show
183 311 gm
(0.75)show
183 347 gm
(0.93)show
183 383 gm
(0.23)show
183 442 gm
(2382)show
183 503 gm
(3.70)show
171 82 gm
0 gr
171 82 lin
171 80 gm
171 80 lin
171 83 gm
171 128 lin
171 131 gm
171 131 lin
171 129 gm
171 129 lin
171 132 gm
171 175 lin
171 178 gm
171 178 lin
171 176 gm
171 176 lin
171 179 gm
171 232 lin
171 235 gm
171 235 lin
171 233 gm
171 233 lin
171 236 gm
171 266 lin
171 269 gm
171 269 lin
171 267 gm
171 267 lin
171 270 gm
171 300 lin
171 303 gm
171 303 lin
171 301 gm
171 301 lin
171 304 gm
171 334 lin
171 337 gm
171 337 lin
171 335 gm
171 335 lin
171 338 gm
171 372 lin
171 375 gm
171 375 lin
171 373 gm
171 373 lin
171 376 gm
171 406 lin
171 409 gm
171 409 lin
171 407 gm
171 407 lin
171 410 gm
171 492 lin
171 495 gm
171 495 lin
171 493 gm
171 493 lin
171 496 gm
171 526 lin
171 529 gm
171 529 lin
171 527 gm
171 527 lin
172 80 gm
185 80 lin
172 82 gm
185 82 lin
172 129 gm
185 129 lin
172 131 gm
185 131 lin
172 176 gm
185 176 lin
172 178 gm
185 178 lin
172 233 gm
185 233 lin
172 235 gm
185 235 lin
172 267 gm
185 267 lin
172 269 gm
185 269 lin
172 301 gm
185 301 lin
172 303 gm
185 303 lin
172 335 gm
185 335 lin
172 337 gm
185 337 lin
172 373 gm
185 373 lin
172 375 gm
185 375 lin
172 407 gm
185 407 lin
172 409 gm
185 409 lin
172 493 gm
185 493 lin
172 495 gm
185 495 lin
172 527 gm
185 527 lin
172 529 gm
185 529 lin
198 104 gm
F 1 setTxMode
(7)show
198 144 gm
(2242)show
198 189 gm
(7236560)show
198 243 gm
(3.70)show
198 277 gm
(0.53)show
198 311 gm
(0.71)show
198 347 gm
(0.83)show
198 383 gm
(0.35)show
198 442 gm
(3228)show
198 503 gm
(5.01)show
186 82 gm
0 gr
186 82 lin
186 80 gm
186 80 lin
186 83 gm
186 128 lin
186 131 gm
186 131 lin
186 129 gm
186 129 lin
186 132 gm
186 175 lin
186 178 gm
186 178 lin
186 176 gm
186 176 lin
186 179 gm
186 232 lin
186 235 gm
186 235 lin
186 233 gm
186 233 lin
186 236 gm
186 266 lin
186 269 gm
186 269 lin
186 267 gm
186 267 lin
186 270 gm
186 300 lin
186 303 gm
186 303 lin
186 301 gm
186 301 lin
186 304 gm
186 334 lin
186 337 gm
186 337 lin
186 335 gm
186 335 lin
186 338 gm
186 372 lin
186 375 gm
186 375 lin
186 373 gm
186 373 lin
186 376 gm
186 406 lin
186 409 gm
186 409 lin
186 407 gm
186 407 lin
186 410 gm
186 492 lin
186 495 gm
186 495 lin
186 493 gm
186 493 lin
186 496 gm
186 526 lin
186 529 gm
186 529 lin
186 527 gm
186 527 lin
187 80 gm
200 80 lin
187 82 gm
200 82 lin
187 129 gm
200 129 lin
187 131 gm
200 131 lin
187 176 gm
200 176 lin
187 178 gm
200 178 lin
187 233 gm
200 233 lin
187 235 gm
200 235 lin
187 267 gm
200 267 lin
187 269 gm
200 269 lin
187 301 gm
200 301 lin
187 303 gm
200 303 lin
187 335 gm
200 335 lin
187 337 gm
200 337 lin
187 373 gm
200 373 lin
187 375 gm
200 375 lin
187 407 gm
200 407 lin
187 409 gm
200 409 lin
187 493 gm
200 493 lin
187 495 gm
200 495 lin
187 527 gm
200 527 lin
187 529 gm
200 529 lin
213 104 gm
F 1 setTxMode
(9)show
213 144 gm
(1988)show
213 189 gm
(7876769)show
213 243 gm
(4.18)show
213 277 gm
(0.46)show
213 311 gm
(0.68)show
213 347 gm
(0.77)show
213 383 gm
(0.47)show
213 442 gm
(3962)show
213 503 gm
(6.15)show
201 82 gm
0 gr
201 82 lin
201 80 gm
201 80 lin
201 83 gm
201 128 lin
201 131 gm
201 131 lin
201 129 gm
201 129 lin
201 132 gm
201 175 lin
201 178 gm
201 178 lin
201 176 gm
201 176 lin
201 179 gm
201 232 lin
201 235 gm
201 235 lin
201 233 gm
201 233 lin
201 236 gm
201 266 lin
201 269 gm
201 269 lin
201 267 gm
201 267 lin
201 270 gm
201 300 lin
201 303 gm
201 303 lin
201 301 gm
201 301 lin
201 304 gm
201 334 lin
201 337 gm
201 337 lin
201 335 gm
201 335 lin
201 338 gm
201 372 lin
201 375 gm
201 375 lin
201 373 gm
201 373 lin
201 376 gm
201 406 lin
201 409 gm
201 409 lin
201 407 gm
201 407 lin
201 410 gm
201 492 lin
201 495 gm
201 495 lin
201 493 gm
201 493 lin
201 496 gm
201 526 lin
201 529 gm
201 529 lin
201 527 gm
201 527 lin
202 80 gm
215 80 lin
202 82 gm
215 82 lin
202 129 gm
215 129 lin
202 131 gm
215 131 lin
202 176 gm
215 176 lin
202 178 gm
215 178 lin
202 233 gm
215 233 lin
202 235 gm
215 235 lin
202 267 gm
215 267 lin
202 269 gm
215 269 lin
202 301 gm
215 301 lin
202 303 gm
215 303 lin
202 335 gm
215 335 lin
202 337 gm
215 337 lin
202 373 gm
215 373 lin
202 375 gm
215 375 lin
202 407 gm
215 407 lin
202 409 gm
215 409 lin
202 493 gm
215 493 lin
202 495 gm
215 495 lin
202 527 gm
215 527 lin
202 529 gm
215 529 lin
228 101 gm
F 1 setTxMode
(11)show
228 144 gm
(1786)show
228 189 gm
(8521288)show
228 243 gm
(4.65)show
228 277 gm
(0.42)show
228 311 gm
(0.66)show
228 347 gm
(0.73)show
228 383 gm
(0.59)show
228 442 gm
(4771)show
228 503 gm
(7.41)show
216 82 gm
0 gr
216 82 lin
216 80 gm
216 80 lin
216 83 gm
216 128 lin
216 131 gm
216 131 lin
216 129 gm
216 129 lin
216 132 gm
216 175 lin
216 178 gm
216 178 lin
216 176 gm
216 176 lin
216 179 gm
216 232 lin
216 235 gm
216 235 lin
216 233 gm
216 233 lin
216 236 gm
216 266 lin
216 269 gm
216 269 lin
216 267 gm
216 267 lin
216 270 gm
216 300 lin
216 303 gm
216 303 lin
216 301 gm
216 301 lin
216 304 gm
216 334 lin
216 337 gm
216 337 lin
216 335 gm
216 335 lin
216 338 gm
216 372 lin
216 375 gm
216 375 lin
216 373 gm
216 373 lin
216 376 gm
216 406 lin
216 409 gm
216 409 lin
216 407 gm
216 407 lin
216 410 gm
216 492 lin
216 495 gm
216 495 lin
216 493 gm
216 493 lin
216 496 gm
216 526 lin
216 529 gm
216 529 lin
216 527 gm
216 527 lin
217 80 gm
230 80 lin
217 82 gm
230 82 lin
233 80 gm
233 82 lin
231 80 gm
233 80 lin
231 82 gm
231 82 lin
231 82 lin
231 83 gm
231 128 lin
233 83 gm
233 128 lin
217 129 gm
230 129 lin
217 131 gm
230 131 lin
231 129 gm
231 131 lin
233 129 gm
233 131 lin
231 132 gm
231 175 lin
233 132 gm
233 175 lin
217 176 gm
230 176 lin
217 178 gm
230 178 lin
231 176 gm
231 178 lin
233 176 gm
233 178 lin
231 179 gm
231 232 lin
233 179 gm
233 232 lin
217 233 gm
230 233 lin
217 235 gm
230 235 lin
231 233 gm
231 235 lin
233 233 gm
233 235 lin
231 236 gm
231 266 lin
233 236 gm
233 266 lin
217 267 gm
230 267 lin
217 269 gm
230 269 lin
231 267 gm
231 269 lin
233 267 gm
233 269 lin
231 270 gm
231 300 lin
233 270 gm
233 300 lin
217 301 gm
230 301 lin
217 303 gm
230 303 lin
231 301 gm
231 303 lin
233 301 gm
233 303 lin
231 304 gm
231 334 lin
233 304 gm
233 334 lin
217 335 gm
230 335 lin
217 337 gm
230 337 lin
231 335 gm
231 337 lin
233 335 gm
233 337 lin
231 338 gm
231 372 lin
233 338 gm
233 372 lin
217 373 gm
230 373 lin
217 375 gm
230 375 lin
231 373 gm
231 375 lin
233 373 gm
233 375 lin
231 376 gm
231 406 lin
233 376 gm
233 406 lin
217 407 gm
230 407 lin
217 409 gm
230 409 lin
231 407 gm
231 409 lin
233 407 gm
233 409 lin
231 410 gm
231 492 lin
233 410 gm
233 492 lin
217 493 gm
230 493 lin
217 495 gm
230 495 lin
231 493 gm
231 495 lin
233 493 gm
233 495 lin
231 496 gm
231 526 lin
233 496 gm
233 526 lin
217 527 gm
230 527 lin
217 529 gm
230 529 lin
233 527 gm
233 529 lin
231 529 gm
233 529 lin
231 527 gm
231 527 lin
231 527 lin
245 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig. 7)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Results of experiments for core algorithm)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( \(basic master worker\))show
261 79 gm
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.32440 0. 32 0.03244 0.(In Fig. 7 we show data for the core algorithm. The reported speedup is low; moreover, values for E)awidthshow
272 79 gm
(tell that adding processors we increase all overheads:)show
284 88 gm
2.20611 0. 32 0.22061 0.(\245\312search overhead: compare real speedup S with ideal speedup S)awidthshow
284 403 gm
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.49050 0.(ss)ashow
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
2.22335 0. 32 0.22233 0.(. For instance, with 11)awidthshow
295 101 gm
2.43774 0. 32 0.24377 0.(processors we have a 37% loss \(S)awidthshow
295 271 gm
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.33930 0.(ss)ashow
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
2.01950 0. 32 0.20195 0.(=7.41\312vs\312S=4.65\). This loss is caused by minimum)awidthshow
306 101 gm
0.54733 0. 32 0.05473 0.(cooperation. We also remark that search overhead increases with more processors because all)awidthshow
317 101 gm
0.40542 0. 32 0.04054 0.(workers start with value = -)awidthshow
currentfont SwToSym
0.40542 0. 32 0.04054 0.(\245)awidthshow
setfont
0.40542 0. 32 0.04054 0.( , whereas the sequential search has a good approximation of the)awidthshow
328 101 gm
(value starting from the second subtree.)show
341 88 gm
1.70776 0. 32 0.17077 0.(\245\312communication and synchronization overhead: F)awidthshow
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.38545 0.(pm)ashow
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
1.18698 0. 32 0.11869 0.( increases until 5 processors \(75%\) then)awidthshow
352 101 gm
0.20828 0. 32 0.02082 0.(decreases; for 11 processors the F)awidthshow
352 251 gm
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.07923 0.(pm)ashow
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.21224 0. 32 0.02122 0.( value is almost the same as with 3 processors \(66%\). This)awidthshow
363 101 gm
0.66604 0. 32 0.06660 0.(is explained by the fact that the master is idle most of the time, so if we use one process per)awidthshow
374 101 gm
(processor a processor is idle as well.)show
404 96 gm
1 fs
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(Procs)show
404 145 gm
(T\312\(sec\))show
404 200 gm
(N\312\(nodes\))show
404 271 gm
(S)show
404 308 gm
(E)show
404 338 gm
(Fpm)show
404 378 gm
(SO)show
404 416 gm
(SS\312\(nodes/sec\))show
404 502 gm
(Sss)show
390 80 gm
0 gr
390 82 lin
390 80 gm
392 80 lin
392 82 gm
392 82 lin
392 82 lin
390 83 gm
390 131 lin
392 83 gm
392 131 lin
390 132 gm
390 134 lin
392 132 gm
392 134 lin
390 135 gm
390 182 lin
392 135 gm
392 182 lin
390 183 gm
390 185 lin
392 183 gm
392 185 lin
390 186 gm
390 253 lin
392 186 gm
392 253 lin
390 254 gm
390 256 lin
392 254 gm
392 256 lin
390 257 gm
390 290 lin
392 257 gm
392 290 lin
390 291 gm
390 293 lin
392 291 gm
392 293 lin
390 294 gm
390 327 lin
392 294 gm
392 327 lin
390 328 gm
390 330 lin
392 328 gm
392 330 lin
390 331 gm
390 364 lin
392 331 gm
392 364 lin
390 365 gm
390 367 lin
392 365 gm
392 367 lin
390 368 gm
390 400 lin
392 368 gm
392 400 lin
390 401 gm
390 403 lin
392 401 gm
392 403 lin
390 404 gm
390 487 lin
392 404 gm
392 487 lin
390 488 gm
390 490 lin
392 488 gm
392 490 lin
390 491 gm
390 524 lin
392 491 gm
392 524 lin
390 525 gm
390 527 lin
392 527 lin
392 525 gm
392 525 lin
392 525 lin
393 80 gm
406 80 lin
393 82 gm
406 82 lin
393 132 gm
406 132 lin
393 134 gm
406 134 lin
393 183 gm
406 183 lin
393 185 gm
406 185 lin
393 254 gm
406 254 lin
393 256 gm
406 256 lin
393 291 gm
406 291 lin
393 293 gm
406 293 lin
393 328 gm
406 328 lin
393 330 gm
406 330 lin
393 365 gm
406 365 lin
393 367 gm
406 367 lin
393 401 gm
406 401 lin
393 403 gm
406 403 lin
393 488 gm
406 488 lin
393 490 gm
406 490 lin
393 525 gm
406 525 lin
393 527 gm
406 527 lin
421 105 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
421 149 gm
(8301)show
421 203 gm
(5347545)show
421 269 gm
(---)show
421 306 gm
(---)show
421 343 gm
(---)show
421 380 gm
(---)show
421 439 gm
(644)show
421 503 gm
(---)show
407 82 gm
0 gr
409 82 lin
407 80 gm
409 80 lin
407 83 gm
407 131 lin
409 83 gm
409 131 lin
407 134 gm
407 134 lin
409 132 gm
409 132 lin
407 132 gm
407 132 lin
409 134 gm
409 134 lin
407 135 gm
407 182 lin
409 135 gm
409 182 lin
407 185 gm
407 185 lin
409 183 gm
409 183 lin
407 183 gm
407 183 lin
409 185 gm
409 185 lin
407 186 gm
407 253 lin
409 186 gm
409 253 lin
407 256 gm
407 256 lin
409 254 gm
409 254 lin
407 254 gm
407 254 lin
409 256 gm
409 256 lin
407 257 gm
407 290 lin
409 257 gm
409 290 lin
407 293 gm
407 293 lin
409 291 gm
409 291 lin
407 291 gm
407 291 lin
409 293 gm
409 293 lin
407 294 gm
407 327 lin
409 294 gm
409 327 lin
407 330 gm
407 330 lin
409 328 gm
409 328 lin
407 328 gm
407 328 lin
409 330 gm
409 330 lin
407 331 gm
407 364 lin
409 331 gm
409 364 lin
407 367 gm
407 367 lin
409 365 gm
409 365 lin
407 365 gm
407 365 lin
409 367 gm
409 367 lin
407 368 gm
407 400 lin
409 368 gm
409 400 lin
407 403 gm
407 403 lin
409 401 gm
409 401 lin
407 401 gm
407 401 lin
409 403 gm
409 403 lin
407 404 gm
407 487 lin
409 404 gm
409 487 lin
407 490 gm
407 490 lin
409 488 gm
409 488 lin
407 488 gm
407 488 lin
409 490 gm
409 490 lin
407 491 gm
407 524 lin
409 491 gm
409 524 lin
407 527 gm
409 527 lin
407 525 gm
409 525 lin
410 80 gm
423 80 lin
410 82 gm
423 82 lin
410 132 gm
423 132 lin
410 134 gm
423 134 lin
410 183 gm
423 183 lin
410 185 gm
423 185 lin
410 254 gm
423 254 lin
410 256 gm
423 256 lin
410 291 gm
423 291 lin
410 293 gm
423 293 lin
410 328 gm
423 328 lin
410 330 gm
423 330 lin
410 365 gm
423 365 lin
410 367 gm
423 367 lin
410 401 gm
423 401 lin
410 403 gm
423 403 lin
410 488 gm
423 488 lin
410 490 gm
423 490 lin
410 525 gm
423 525 lin
410 527 gm
423 527 lin
436 105 gm
F 1 setTxMode
(3)show
436 149 gm
(4544)show
436 203 gm
(5860668)show
436 265 gm
(1.83)show
436 302 gm
(0.61)show
436 339 gm
(0.70)show
436 376 gm
(0.10)show
436 436 gm
(1290)show
436 499 gm
(2.00)show
424 82 gm
0 gr
424 82 lin
424 80 gm
424 80 lin
424 83 gm
424 131 lin
424 134 gm
424 134 lin
424 132 gm
424 132 lin
424 135 gm
424 182 lin
424 185 gm
424 185 lin
424 183 gm
424 183 lin
424 186 gm
424 253 lin
424 256 gm
424 256 lin
424 254 gm
424 254 lin
424 257 gm
424 290 lin
424 293 gm
424 293 lin
424 291 gm
424 291 lin
424 294 gm
424 327 lin
424 330 gm
424 330 lin
424 328 gm
424 328 lin
424 331 gm
424 364 lin
424 367 gm
424 367 lin
424 365 gm
424 365 lin
424 368 gm
424 400 lin
424 403 gm
424 403 lin
424 401 gm
424 401 lin
424 404 gm
424 487 lin
424 490 gm
424 490 lin
424 488 gm
424 488 lin
424 491 gm
424 524 lin
424 527 gm
424 527 lin
424 525 gm
424 525 lin
425 80 gm
438 80 lin
425 82 gm
438 82 lin
425 132 gm
438 132 lin
425 134 gm
438 134 lin
425 183 gm
438 183 lin
425 185 gm
438 185 lin
425 254 gm
438 254 lin
425 256 gm
438 256 lin
425 291 gm
438 291 lin
425 293 gm
438 293 lin
425 328 gm
438 328 lin
425 330 gm
438 330 lin
425 365 gm
438 365 lin
425 367 gm
438 367 lin
425 401 gm
438 401 lin
425 403 gm
438 403 lin
425 488 gm
438 488 lin
425 490 gm
438 490 lin
425 525 gm
438 525 lin
425 527 gm
438 527 lin
451 105 gm
F 1 setTxMode
(5)show
451 149 gm
(3173)show
451 203 gm
(6330053)show
451 265 gm
(2.62)show
451 302 gm
(0.52)show
451 339 gm
(0.66)show
451 376 gm
(0.18)show
451 436 gm
(1995)show
451 499 gm
(3.10)show
439 82 gm
0 gr
439 82 lin
439 80 gm
439 80 lin
439 83 gm
439 131 lin
439 134 gm
439 134 lin
439 132 gm
439 132 lin
439 135 gm
439 182 lin
439 185 gm
439 185 lin
439 183 gm
439 183 lin
439 186 gm
439 253 lin
439 256 gm
439 256 lin
439 254 gm
439 254 lin
439 257 gm
439 290 lin
439 293 gm
439 293 lin
439 291 gm
439 291 lin
439 294 gm
439 327 lin
439 330 gm
439 330 lin
439 328 gm
439 328 lin
439 331 gm
439 364 lin
439 367 gm
439 367 lin
439 365 gm
439 365 lin
439 368 gm
439 400 lin
439 403 gm
439 403 lin
439 401 gm
439 401 lin
439 404 gm
439 487 lin
439 490 gm
439 490 lin
439 488 gm
439 488 lin
439 491 gm
439 524 lin
439 527 gm
439 527 lin
439 525 gm
439 525 lin
440 80 gm
453 80 lin
440 82 gm
453 82 lin
440 132 gm
453 132 lin
440 134 gm
453 134 lin
440 183 gm
453 183 lin
440 185 gm
453 185 lin
440 254 gm
453 254 lin
440 256 gm
453 256 lin
440 291 gm
453 291 lin
440 293 gm
453 293 lin
440 328 gm
453 328 lin
440 330 gm
453 330 lin
440 365 gm
453 365 lin
440 367 gm
453 367 lin
440 401 gm
453 401 lin
440 403 gm
453 403 lin
440 488 gm
453 488 lin
440 490 gm
453 490 lin
440 525 gm
453 525 lin
440 527 gm
453 527 lin
466 105 gm
F 1 setTxMode
(7)show
466 149 gm
(2779)show
466 203 gm
(6867688)show
466 265 gm
(2.99)show
466 302 gm
(0.43)show
466 339 gm
(0.61)show
466 376 gm
(0.28)show
466 436 gm
(2471)show
466 499 gm
(3.84)show
454 82 gm
0 gr
454 82 lin
454 80 gm
454 80 lin
454 83 gm
454 131 lin
454 134 gm
454 134 lin
454 132 gm
454 132 lin
454 135 gm
454 182 lin
454 185 gm
454 185 lin
454 183 gm
454 183 lin
454 186 gm
454 253 lin
454 256 gm
454 256 lin
454 254 gm
454 254 lin
454 257 gm
454 290 lin
454 293 gm
454 293 lin
454 291 gm
454 291 lin
454 294 gm
454 327 lin
454 330 gm
454 330 lin
454 328 gm
454 328 lin
454 331 gm
454 364 lin
454 367 gm
454 367 lin
454 365 gm
454 365 lin
454 368 gm
454 400 lin
454 403 gm
454 403 lin
454 401 gm
454 401 lin
454 404 gm
454 487 lin
454 490 gm
454 490 lin
454 488 gm
454 488 lin
454 491 gm
454 524 lin
454 527 gm
454 527 lin
454 525 gm
454 525 lin
455 80 gm
468 80 lin
455 82 gm
468 82 lin
455 132 gm
468 132 lin
455 134 gm
468 134 lin
455 183 gm
468 183 lin
455 185 gm
468 185 lin
455 254 gm
468 254 lin
455 256 gm
468 256 lin
455 291 gm
468 291 lin
455 293 gm
468 293 lin
455 328 gm
468 328 lin
455 330 gm
468 330 lin
455 365 gm
468 365 lin
455 367 gm
468 367 lin
455 401 gm
468 401 lin
455 403 gm
468 403 lin
455 488 gm
468 488 lin
455 490 gm
468 490 lin
455 525 gm
468 525 lin
455 527 gm
468 527 lin
481 105 gm
F 1 setTxMode
(9)show
481 149 gm
(2517)show
481 203 gm
(7310806)show
481 265 gm
(3.30)show
481 302 gm
(0.37)show
481 339 gm
(0.57)show
481 376 gm
(0.37)show
481 436 gm
(2905)show
481 499 gm
(4.51)show
469 82 gm
0 gr
469 82 lin
469 80 gm
469 80 lin
469 83 gm
469 131 lin
469 134 gm
469 134 lin
469 132 gm
469 132 lin
469 135 gm
469 182 lin
469 185 gm
469 185 lin
469 183 gm
469 183 lin
469 186 gm
469 253 lin
469 256 gm
469 256 lin
469 254 gm
469 254 lin
469 257 gm
469 290 lin
469 293 gm
469 293 lin
469 291 gm
469 291 lin
469 294 gm
469 327 lin
469 330 gm
469 330 lin
469 328 gm
469 328 lin
469 331 gm
469 364 lin
469 367 gm
469 367 lin
469 365 gm
469 365 lin
469 368 gm
469 400 lin
469 403 gm
469 403 lin
469 401 gm
469 401 lin
469 404 gm
469 487 lin
469 490 gm
469 490 lin
469 488 gm
469 488 lin
469 491 gm
469 524 lin
469 527 gm
469 527 lin
469 525 gm
469 525 lin
470 80 gm
483 80 lin
470 82 gm
483 82 lin
470 132 gm
483 132 lin
470 134 gm
483 134 lin
470 183 gm
483 183 lin
470 185 gm
483 185 lin
470 254 gm
483 254 lin
470 256 gm
483 256 lin
470 291 gm
483 291 lin
470 293 gm
483 293 lin
470 328 gm
483 328 lin
470 330 gm
483 330 lin
470 365 gm
483 365 lin
470 367 gm
483 367 lin
470 401 gm
483 401 lin
470 403 gm
483 403 lin
470 488 gm
483 488 lin
470 490 gm
483 490 lin
470 525 gm
483 525 lin
470 527 gm
483 527 lin
496 103 gm
F 1 setTxMode
(11)show
496 149 gm
(2310)show
496 203 gm
(7990369)show
496 265 gm
(3.59)show
496 302 gm
(0.33)show
496 339 gm
(0.54)show
496 376 gm
(0.49)show
496 436 gm
(3459)show
496 499 gm
(5.37)show
484 82 gm
0 gr
484 82 lin
484 80 gm
484 80 lin
484 83 gm
484 131 lin
484 134 gm
484 134 lin
484 132 gm
484 132 lin
484 135 gm
484 182 lin
484 185 gm
484 185 lin
484 183 gm
484 183 lin
484 186 gm
484 253 lin
484 256 gm
484 256 lin
484 254 gm
484 254 lin
484 257 gm
484 290 lin
484 293 gm
484 293 lin
484 291 gm
484 291 lin
484 294 gm
484 327 lin
484 330 gm
484 330 lin
484 328 gm
484 328 lin
484 331 gm
484 364 lin
484 367 gm
484 367 lin
484 365 gm
484 365 lin
484 368 gm
484 400 lin
484 403 gm
484 403 lin
484 401 gm
484 401 lin
484 404 gm
484 487 lin
484 490 gm
484 490 lin
484 488 gm
484 488 lin
484 491 gm
484 524 lin
484 527 gm
484 527 lin
484 525 gm
484 525 lin
485 80 gm
498 80 lin
485 82 gm
498 82 lin
501 80 gm
501 82 lin
499 80 gm
501 80 lin
499 82 gm
499 82 lin
499 82 lin
499 83 gm
499 131 lin
501 83 gm
501 131 lin
485 132 gm
498 132 lin
485 134 gm
498 134 lin
499 132 gm
499 134 lin
501 132 gm
501 134 lin
499 135 gm
499 182 lin
501 135 gm
501 182 lin
485 183 gm
498 183 lin
485 185 gm
498 185 lin
499 183 gm
499 185 lin
501 183 gm
501 185 lin
499 186 gm
499 253 lin
501 186 gm
501 253 lin
485 254 gm
498 254 lin
485 256 gm
498 256 lin
499 254 gm
499 256 lin
501 254 gm
501 256 lin
499 257 gm
499 290 lin
501 257 gm
501 290 lin
485 291 gm
498 291 lin
485 293 gm
498 293 lin
499 291 gm
499 293 lin
501 291 gm
501 293 lin
499 294 gm
499 327 lin
501 294 gm
501 327 lin
485 328 gm
498 328 lin
485 330 gm
498 330 lin
499 328 gm
499 330 lin
501 328 gm
501 330 lin
499 331 gm
499 364 lin
501 331 gm
501 364 lin
485 365 gm
498 365 lin
485 367 gm
498 367 lin
499 365 gm
499 367 lin
501 365 gm
501 367 lin
499 368 gm
499 400 lin
501 368 gm
501 400 lin
485 401 gm
498 401 lin
485 403 gm
498 403 lin
499 401 gm
499 403 lin
501 401 gm
501 403 lin
499 404 gm
499 487 lin
501 404 gm
501 487 lin
485 488 gm
498 488 lin
485 490 gm
498 490 lin
499 488 gm
499 490 lin
501 488 gm
501 490 lin
499 491 gm
499 524 lin
501 491 gm
501 524 lin
485 525 gm
498 525 lin
485 527 gm
498 527 lin
501 525 gm
501 527 lin
499 527 gm
501 527 lin
499 525 gm
499 525 lin
499 525 lin
513 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(.)show
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(8)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Static splitting, master does part of  the search)show
530 101 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.02517 0. 32 0.00251 0.(We should allocate a worker on the master processor; unfortunately, Fig.8 shows that this is not)awidthshow
541 101 gm
0.28411 0. 32 0.02841 0.(a good idea, because a master process should be able to generate new tasks rapidly when other)awidthshow
552 101 gm
1.02462 0. 32 0.10246 0.(processors become idle: when a processor is shared by the master and a worker the answer)awidthshow
563 101 gm
(times for master become too slow.)show
593 96 gm
1 fs
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(Procs)show
593 145 gm
(T\312\(sec\))show
593 203 gm
(N\312\(nodi\))show
593 271 gm
(S)show
593 308 gm
(E)show
593 338 gm
(Fpm)show
593 378 gm
(SO)show
593 419 gm
(SS\312\(nodi/sec\))show
593 502 gm
(Sss)show
579 80 gm
0 gr
579 82 lin
579 80 gm
581 80 lin
581 82 gm
581 82 lin
581 82 lin
579 83 gm
579 131 lin
581 83 gm
581 131 lin
579 132 gm
579 134 lin
581 132 gm
581 134 lin
579 135 gm
579 182 lin
581 135 gm
581 182 lin
579 183 gm
579 185 lin
581 183 gm
581 185 lin
579 186 gm
579 253 lin
581 186 gm
581 253 lin
579 254 gm
579 256 lin
581 254 gm
581 256 lin
579 257 gm
579 290 lin
581 257 gm
581 290 lin
579 291 gm
579 293 lin
581 291 gm
581 293 lin
579 294 gm
579 327 lin
581 294 gm
581 327 lin
579 328 gm
579 330 lin
581 328 gm
581 330 lin
579 331 gm
579 364 lin
581 331 gm
581 364 lin
579 365 gm
579 367 lin
581 365 gm
581 367 lin
579 368 gm
579 400 lin
581 368 gm
581 400 lin
579 401 gm
579 403 lin
581 401 gm
581 403 lin
579 404 gm
579 487 lin
581 404 gm
581 487 lin
579 488 gm
579 490 lin
581 488 gm
581 490 lin
579 491 gm
579 524 lin
581 491 gm
581 524 lin
579 525 gm
579 527 lin
581 527 lin
581 525 gm
581 525 lin
581 525 lin
582 80 gm
595 80 lin
582 82 gm
595 82 lin
582 132 gm
595 132 lin
582 134 gm
595 134 lin
582 183 gm
595 183 lin
582 185 gm
595 185 lin
582 254 gm
595 254 lin
582 256 gm
595 256 lin
582 291 gm
595 291 lin
582 293 gm
595 293 lin
582 328 gm
595 328 lin
582 330 gm
595 330 lin
582 365 gm
595 365 lin
582 367 gm
595 367 lin
582 401 gm
595 401 lin
582 403 gm
595 403 lin
582 488 gm
595 488 lin
582 490 gm
595 490 lin
582 525 gm
595 525 lin
582 527 gm
595 527 lin
610 105 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
610 149 gm
(8301)show
610 203 gm
(5347545)show
610 269 gm
(---)show
610 306 gm
(---)show
610 343 gm
(---)show
610 380 gm
(---)show
610 439 gm
(644)show
610 503 gm
(---)show
596 82 gm
0 gr
598 82 lin
596 80 gm
598 80 lin
596 83 gm
596 131 lin
598 83 gm
598 131 lin
596 134 gm
596 134 lin
598 132 gm
598 132 lin
596 132 gm
596 132 lin
598 134 gm
598 134 lin
596 135 gm
596 182 lin
598 135 gm
598 182 lin
596 185 gm
596 185 lin
598 183 gm
598 183 lin
596 183 gm
596 183 lin
598 185 gm
598 185 lin
596 186 gm
596 253 lin
598 186 gm
598 253 lin
596 256 gm
596 256 lin
598 254 gm
598 254 lin
596 254 gm
596 254 lin
598 256 gm
598 256 lin
596 257 gm
596 290 lin
598 257 gm
598 290 lin
596 293 gm
596 293 lin
598 291 gm
598 291 lin
596 291 gm
596 291 lin
598 293 gm
598 293 lin
596 294 gm
596 327 lin
598 294 gm
598 327 lin
596 330 gm
596 330 lin
598 328 gm
598 328 lin
596 328 gm
596 328 lin
598 330 gm
598 330 lin
596 331 gm
596 364 lin
598 331 gm
598 364 lin
596 367 gm
596 367 lin
598 365 gm
598 365 lin
596 365 gm
596 365 lin
598 367 gm
598 367 lin
596 368 gm
596 400 lin
598 368 gm
598 400 lin
596 403 gm
596 403 lin
598 401 gm
598 401 lin
596 401 gm
596 401 lin
598 403 gm
598 403 lin
596 404 gm
596 487 lin
598 404 gm
598 487 lin
596 490 gm
596 490 lin
598 488 gm
598 488 lin
596 488 gm
596 488 lin
598 490 gm
598 490 lin
596 491 gm
596 524 lin
598 491 gm
598 524 lin
596 527 gm
598 527 lin
596 525 gm
598 525 lin
599 80 gm
612 80 lin
599 82 gm
612 82 lin
599 132 gm
612 132 lin
599 134 gm
612 134 lin
599 183 gm
612 183 lin
599 185 gm
612 185 lin
599 254 gm
612 254 lin
599 256 gm
612 256 lin
599 291 gm
612 291 lin
599 293 gm
612 293 lin
599 328 gm
612 328 lin
599 330 gm
612 330 lin
599 365 gm
612 365 lin
599 367 gm
612 367 lin
599 401 gm
612 401 lin
599 403 gm
612 403 lin
599 488 gm
612 488 lin
599 490 gm
612 490 lin
599 525 gm
612 525 lin
599 527 gm
612 527 lin
625 105 gm
F 1 setTxMode
(3)show
625 149 gm
(3298)show
625 203 gm
(6156027)show
625 265 gm
(2.52)show
625 302 gm
(0.84)show
625 339 gm
(0.96)show
625 376 gm
(0.15)show
625 436 gm
(1867)show
625 499 gm
(2.90)show
613 82 gm
0 gr
613 82 lin
613 80 gm
613 80 lin
613 83 gm
613 131 lin
613 134 gm
613 134 lin
613 132 gm
613 132 lin
613 135 gm
613 182 lin
613 185 gm
613 185 lin
613 183 gm
613 183 lin
613 186 gm
613 253 lin
613 256 gm
613 256 lin
613 254 gm
613 254 lin
613 257 gm
613 290 lin
613 293 gm
613 293 lin
613 291 gm
613 291 lin
613 294 gm
613 327 lin
613 330 gm
613 330 lin
613 328 gm
613 328 lin
613 331 gm
613 364 lin
613 367 gm
613 367 lin
613 365 gm
613 365 lin
613 368 gm
613 400 lin
613 403 gm
613 403 lin
613 401 gm
613 401 lin
613 404 gm
613 487 lin
613 490 gm
613 490 lin
613 488 gm
613 488 lin
613 491 gm
613 524 lin
613 527 gm
613 527 lin
613 525 gm
613 525 lin
614 80 gm
627 80 lin
614 82 gm
627 82 lin
614 132 gm
627 132 lin
614 134 gm
627 134 lin
614 183 gm
627 183 lin
614 185 gm
627 185 lin
614 254 gm
627 254 lin
614 256 gm
627 256 lin
614 291 gm
627 291 lin
614 293 gm
627 293 lin
614 328 gm
627 328 lin
614 330 gm
627 330 lin
614 365 gm
627 365 lin
614 367 gm
627 367 lin
614 401 gm
627 401 lin
614 403 gm
627 403 lin
614 488 gm
627 488 lin
614 490 gm
627 490 lin
614 525 gm
627 525 lin
614 527 gm
627 527 lin
640 105 gm
F 1 setTxMode
(5)show
640 149 gm
(2382)show
640 203 gm
(6945194)show
640 265 gm
(3.48)show
640 302 gm
(0.70)show
640 339 gm
(0.91)show
640 376 gm
(0.30)show
640 436 gm
(2916)show
640 499 gm
(4.53)show
628 82 gm
0 gr
628 82 lin
628 80 gm
628 80 lin
628 83 gm
628 131 lin
628 134 gm
628 134 lin
628 132 gm
628 132 lin
628 135 gm
628 182 lin
628 185 gm
628 185 lin
628 183 gm
628 183 lin
628 186 gm
628 253 lin
628 256 gm
628 256 lin
628 254 gm
628 254 lin
628 257 gm
628 290 lin
628 293 gm
628 293 lin
628 291 gm
628 291 lin
628 294 gm
628 327 lin
628 330 gm
628 330 lin
628 328 gm
628 328 lin
628 331 gm
628 364 lin
628 367 gm
628 367 lin
628 365 gm
628 365 lin
628 368 gm
628 400 lin
628 403 gm
628 403 lin
628 401 gm
628 401 lin
628 404 gm
628 487 lin
628 490 gm
628 490 lin
628 488 gm
628 488 lin
628 491 gm
628 524 lin
628 527 gm
628 527 lin
628 525 gm
628 525 lin
629 80 gm
642 80 lin
629 82 gm
642 82 lin
629 132 gm
642 132 lin
629 134 gm
642 134 lin
629 183 gm
642 183 lin
629 185 gm
642 185 lin
629 254 gm
642 254 lin
629 256 gm
642 256 lin
629 291 gm
642 291 lin
629 293 gm
642 293 lin
629 328 gm
642 328 lin
629 330 gm
642 330 lin
629 365 gm
642 365 lin
629 367 gm
642 367 lin
629 401 gm
642 401 lin
629 403 gm
642 403 lin
629 488 gm
642 488 lin
629 490 gm
642 490 lin
629 525 gm
642 525 lin
629 527 gm
642 527 lin
655 105 gm
F 1 setTxMode
(7)show
655 149 gm
(2064)show
655 203 gm
(7524137)show
655 265 gm
(4.02)show
655 302 gm
(0.57)show
655 339 gm
(0.81)show
655 376 gm
(0.41)show
655 436 gm
(3645)show
655 499 gm
(5.66)show
643 82 gm
0 gr
643 82 lin
643 80 gm
643 80 lin
643 83 gm
643 131 lin
643 134 gm
643 134 lin
643 132 gm
643 132 lin
643 135 gm
643 182 lin
643 185 gm
643 185 lin
643 183 gm
643 183 lin
643 186 gm
643 253 lin
643 256 gm
643 256 lin
643 254 gm
643 254 lin
643 257 gm
643 290 lin
643 293 gm
643 293 lin
643 291 gm
643 291 lin
643 294 gm
643 327 lin
643 330 gm
643 330 lin
643 328 gm
643 328 lin
643 331 gm
643 364 lin
643 367 gm
643 367 lin
643 365 gm
643 365 lin
643 368 gm
643 400 lin
643 403 gm
643 403 lin
643 401 gm
643 401 lin
643 404 gm
643 487 lin
643 490 gm
643 490 lin
643 488 gm
643 488 lin
643 491 gm
643 524 lin
643 527 gm
643 527 lin
643 525 gm
643 525 lin
644 80 gm
657 80 lin
644 82 gm
657 82 lin
644 132 gm
657 132 lin
644 134 gm
657 134 lin
644 183 gm
657 183 lin
644 185 gm
657 185 lin
644 254 gm
657 254 lin
644 256 gm
657 256 lin
644 291 gm
657 291 lin
644 293 gm
657 293 lin
644 328 gm
657 328 lin
644 330 gm
657 330 lin
644 365 gm
657 365 lin
644 367 gm
657 367 lin
644 401 gm
657 401 lin
644 403 gm
657 403 lin
644 488 gm
657 488 lin
644 490 gm
657 490 lin
644 525 gm
657 525 lin
644 527 gm
657 527 lin
670 105 gm
F 1 setTxMode
(9)show
670 149 gm
(1798)show
670 203 gm
(8186074)show
670 265 gm
(4.62)show
670 302 gm
(0.51)show
670 339 gm
(0.77)show
670 376 gm
(0.53)show
670 436 gm
(4553)show
670 499 gm
(7.07)show
658 82 gm
0 gr
658 82 lin
658 80 gm
658 80 lin
658 83 gm
658 131 lin
658 134 gm
658 134 lin
658 132 gm
658 132 lin
658 135 gm
658 182 lin
658 185 gm
658 185 lin
658 183 gm
658 183 lin
658 186 gm
658 253 lin
658 256 gm
658 256 lin
658 254 gm
658 254 lin
658 257 gm
658 290 lin
658 293 gm
658 293 lin
658 291 gm
658 291 lin
658 294 gm
658 327 lin
658 330 gm
658 330 lin
658 328 gm
658 328 lin
658 331 gm
658 364 lin
658 367 gm
658 367 lin
658 365 gm
658 365 lin
658 368 gm
658 400 lin
658 403 gm
658 403 lin
658 401 gm
658 401 lin
658 404 gm
658 487 lin
658 490 gm
658 490 lin
658 488 gm
658 488 lin
658 491 gm
658 524 lin
658 527 gm
658 527 lin
658 525 gm
658 525 lin
659 80 gm
672 80 lin
659 82 gm
672 82 lin
659 132 gm
672 132 lin
659 134 gm
672 134 lin
659 183 gm
672 183 lin
659 185 gm
672 185 lin
659 254 gm
672 254 lin
659 256 gm
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F 1 setTxMode
(11)show
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702 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig.9)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Static splitting, no master  \(democratic cooperation\))show
718 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.72952 0. 32 0.07295 0.(The core algorithm can be rewritten to get a more efficient program: there is no need to maintain)awidthshow
729 79 gm
0.48248 0. 32 0.04824 0.(alive the master if the workers are able to handle the results. We call this variant of master-worker)awidthshow
740 79 gm
-0.00064 0.(\322democratic coperation\323. Data shown in Fig.9 show an improvement with respect to the pure master-)ashow
751 79 gm
0.28015 0. 32 0.02801 0.(worker paradigm. However, such data also show that search overhead increased, because a\) there is)awidthshow
F T cp
%%Page: ? 11
op
30 28 811 566 fr
0 0 xl
1 1 pen
0 0 gm
(nc 0 0 0 0 6 rc)kp
91 336 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0 fs
10 fz
bu fc
2 F /|______Helvetica fnt
bn
(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
773 519 gm
(9)show
118 79 gm
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.70068 0. 32 0.07006 0.(one more process cooperating in the search, and b\) each worker starts executing a new task more)awidthshow
129 79 gm
0.61386 0. 32 0.06138 0.(rapidly, so it is less likely that it can use data from other explorers that finish while it is idle. The)awidthshow
140 79 gm
0.40039 0. 32 0.04003 0.(most important consideration is that the algorithms get similar results as we increase processors. In)awidthshow
151 79 gm
0.63476 0. 32 0.06347 0.(fact, let P be the total number of processors and E\(P\) number of exploring processors; let C\(P\)be:)awidthshow
0 0 pen
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(nc 155 79 185 223 6 rc)kp
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psb
currentpoint
pse
155 79 gm
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psb
30 dict begin
currentpoint 3 -1 roll sub neg 3 1 roll sub 4608 div 960 3 -1 roll exch div scale currentpoint translate 64 44 translate
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/fs 0 def
/sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def
/f1 {findfont dup /cf exch def sf} def
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384 /Times-Roman f1
(C) show
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(\() show
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(P) show
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(=) show
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(E) show
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224 ns
(master) show
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384 ns
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(P) show
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(democratic) show
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384 ns
(\() show
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/thick 0 def
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(-) show
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(1) show
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(P) show
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end
pse
1 1 pen
172 223 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
2.31613 0. 32 0.23161 0.(. The ratio among production factors is proportional to C\(P\),)awidthshow
193 79 gm
4.52468 0. 32 0.45246 0.(whereas the ratio among value of search overhead is inversely proportional; since)awidthshow
0 0 pen
227 265 gm
(nc 197 79 227 265 6 rc)kp
0 gr
227 265 lin
psb
currentpoint
pse
197 79 gm
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psb
30 dict begin
currentpoint 3 -1 roll sub neg 3 1 roll sub 5952 div 960 3 -1 roll exch div scale currentpoint translate 64 44 translate
12 500 moveto
/fs 0 def
/sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def
/f1 {findfont dup /cf exch def sf} def
/ns {cf sf} def
384 /Times-Roman f1
(lim) show
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(p) show
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(\256) show
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(C) show
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(\() show
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(1) show
end
pse
1 1 pen
214 265 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
( the two algorithms are asyntotically equivalent.)show
254 79 gm
1 fs
12 fz
bu fc
2 F /|______Times-Bold fnt
bn
(4.1 Ordered game trees: iterative deepening and top level sorting)show
267 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.68984 0. 32 0.06898 0.(In the algorithms presented above there is no sorting of nodes; however, it is well known that the)awidthshow
282 79 gm
2.09381 0. 32 0.20938 0.(execution of )awidthshow
282 143 gm
bu fc
2 F /|______Symbol fnt
bn
0.69818 0.(ab)ashow
bu fc
2 F /|______Times-Roman fnt
bn
1.98272 0. 32 0.19827 0.( algorithm improves if game tree nodes are ordered [MarCam82]. We have)awidthshow
294 79 gm
0.63858 0. 32 0.06385 0.(implemented such a sorting, and the resulting search algorithm has been tested with the following)awidthshow
305 79 gm
0.10040 0. 32 0.01004 0.(parameters for iterative deepening: INIT=2-plies, MAX=5-plies; thresold for parallel search: 3)awidthshow
305 496 gm
(-plies.)show
320 79 gm
0.18295 0. 32 0.01829 0.(The sequential algorithm we used for comparison is )awidthshow
bu fc
2 F /|______Symbol fnt
bn
0.06732 0.(ab)ashow
bu fc
2 F /|______Times-Roman fnt
bn
0.18188 0. 32 0.01818 0.( with iterative deepening and same INIT and)awidthshow
332 79 gm
(MAX.)show
361 96 gm
1 fs
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(Procs)show
361 145 gm
(T\312\(sec\))show
361 200 gm
(N\312\(nodes\))show
361 271 gm
(S)show
361 308 gm
(E)show
361 338 gm
(Fpm)show
361 378 gm
(SO)show
361 418 gm
(SS )show
9 fz
bu fc
2 F /|______Times-Bold fnt
bn
(\(nodes/sec\))show
361 502 gm
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(Sss)show
347 80 gm
0 gr
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363 80 lin
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363 328 lin
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350 401 gm
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363 403 lin
350 488 gm
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363 525 lin
350 527 gm
363 527 lin
378 105 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
378 149 gm
(6740)show
378 203 gm
(4529971)show
378 269 gm
(---)show
378 306 gm
(---)show
378 343 gm
(---)show
378 380 gm
(---)show
378 439 gm
(672)show
378 503 gm
(---)show
364 82 gm
0 gr
366 82 lin
364 80 gm
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364 290 lin
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364 291 gm
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364 525 gm
366 525 lin
367 80 gm
380 80 lin
367 82 gm
380 82 lin
367 132 gm
380 132 lin
367 134 gm
380 134 lin
367 183 gm
380 183 lin
367 185 gm
380 185 lin
367 254 gm
380 254 lin
367 256 gm
380 256 lin
367 291 gm
380 291 lin
367 293 gm
380 293 lin
367 328 gm
380 328 lin
367 330 gm
380 330 lin
367 365 gm
380 365 lin
367 367 gm
380 367 lin
367 401 gm
380 401 lin
367 403 gm
380 403 lin
367 488 gm
380 488 lin
367 490 gm
380 490 lin
367 525 gm
380 525 lin
367 527 gm
380 527 lin
393 105 gm
F 1 setTxMode
(3)show
393 149 gm
(2884)show
393 203 gm
(5415125)show
393 265 gm
(2.34)show
393 302 gm
(0.78)show
393 339 gm
(0.94)show
393 376 gm
(0.20)show
393 436 gm
(1878)show
393 499 gm
(2.79)show
381 82 gm
0 gr
381 82 lin
381 80 gm
381 80 lin
381 83 gm
381 131 lin
381 134 gm
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381 182 lin
381 185 gm
381 185 lin
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381 186 gm
381 253 lin
381 256 gm
381 256 lin
381 254 gm
381 254 lin
381 257 gm
381 290 lin
381 293 gm
381 293 lin
381 291 gm
381 291 lin
381 294 gm
381 327 lin
381 330 gm
381 330 lin
381 328 gm
381 328 lin
381 331 gm
381 364 lin
381 367 gm
381 367 lin
381 365 gm
381 365 lin
381 368 gm
381 400 lin
381 403 gm
381 403 lin
381 401 gm
381 401 lin
381 404 gm
381 487 lin
381 490 gm
381 490 lin
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381 488 lin
381 491 gm
381 524 lin
381 527 gm
381 527 lin
381 525 gm
381 525 lin
382 80 gm
395 80 lin
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395 82 lin
382 132 gm
395 132 lin
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395 134 lin
382 183 gm
395 183 lin
382 185 gm
395 185 lin
382 254 gm
395 254 lin
382 256 gm
395 256 lin
382 291 gm
395 291 lin
382 293 gm
395 293 lin
382 328 gm
395 328 lin
382 330 gm
395 330 lin
382 365 gm
395 365 lin
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395 367 lin
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395 401 lin
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395 403 lin
382 488 gm
395 488 lin
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395 490 lin
382 525 gm
395 525 lin
382 527 gm
395 527 lin
408 105 gm
F 1 setTxMode
(5)show
408 149 gm
(2229)show
408 203 gm
(6307062)show
408 265 gm
(3.02)show
408 302 gm
(0.60)show
408 339 gm
(0.87)show
408 376 gm
(0.39)show
408 436 gm
(2830)show
408 499 gm
(4.21)show
396 82 gm
0 gr
396 82 lin
396 80 gm
396 80 lin
396 83 gm
396 131 lin
396 134 gm
396 134 lin
396 132 gm
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396 182 lin
396 185 gm
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396 253 lin
396 256 gm
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396 254 gm
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396 257 gm
396 290 lin
396 293 gm
396 293 lin
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396 291 lin
396 294 gm
396 327 lin
396 330 gm
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396 328 gm
396 328 lin
396 331 gm
396 364 lin
396 367 gm
396 367 lin
396 365 gm
396 365 lin
396 368 gm
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410 80 lin
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410 183 lin
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410 328 lin
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410 330 lin
397 365 gm
410 365 lin
397 367 gm
410 367 lin
397 401 gm
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410 403 lin
397 488 gm
410 488 lin
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410 490 lin
397 525 gm
410 525 lin
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410 527 lin
423 105 gm
F 1 setTxMode
(7)show
423 149 gm
(2007)show
423 203 gm
(7317370)show
423 265 gm
(3.36)show
423 302 gm
(0.48)show
423 339 gm
(0.80)show
423 376 gm
(0.62)show
423 436 gm
(3646)show
423 499 gm
(5.42)show
411 82 gm
0 gr
411 82 lin
411 80 gm
411 80 lin
411 83 gm
411 131 lin
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411 132 gm
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411 182 lin
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411 327 lin
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411 527 lin
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412 80 gm
425 80 lin
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425 134 lin
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425 183 lin
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425 254 lin
412 256 gm
425 256 lin
412 291 gm
425 291 lin
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425 293 lin
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425 328 lin
412 330 gm
425 330 lin
412 365 gm
425 365 lin
412 367 gm
425 367 lin
412 401 gm
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425 403 lin
412 488 gm
425 488 lin
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412 525 gm
425 525 lin
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425 527 lin
438 105 gm
F 1 setTxMode
(9)show
438 149 gm
(1839)show
438 203 gm
(8187769)show
438 265 gm
(3.67)show
438 302 gm
(0.41)show
438 339 gm
(0.75)show
438 376 gm
(0.81)show
438 436 gm
(4452)show
438 499 gm
(6.62)show
426 82 gm
0 gr
426 82 lin
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426 80 lin
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427 291 gm
440 291 lin
427 293 gm
440 293 lin
427 328 gm
440 328 lin
427 330 gm
440 330 lin
427 365 gm
440 365 lin
427 367 gm
440 367 lin
427 401 gm
440 401 lin
427 403 gm
440 403 lin
427 488 gm
440 488 lin
427 490 gm
440 490 lin
427 525 gm
440 525 lin
427 527 gm
440 527 lin
453 103 gm
F 1 setTxMode
(11)show
453 149 gm
(1825)show
453 203 gm
(8980505)show
453 265 gm
(3.69)show
453 302 gm
(0.34)show
453 339 gm
(0.71)show
453 376 gm
(0.98)show
453 436 gm
(4921)show
453 499 gm
(7.32)show
441 82 gm
0 gr
441 82 lin
441 80 gm
441 80 lin
441 83 gm
441 131 lin
441 134 gm
441 134 lin
441 132 gm
441 132 lin
441 135 gm
441 182 lin
441 185 gm
441 185 lin
441 183 gm
441 183 lin
441 186 gm
441 253 lin
441 256 gm
441 256 lin
441 254 gm
441 254 lin
441 257 gm
441 290 lin
441 293 gm
441 293 lin
441 291 gm
441 291 lin
441 294 gm
441 327 lin
441 330 gm
441 330 lin
441 328 gm
441 328 lin
441 331 gm
441 364 lin
441 367 gm
441 367 lin
441 365 gm
441 365 lin
441 368 gm
441 400 lin
441 403 gm
441 403 lin
441 401 gm
441 401 lin
441 404 gm
441 487 lin
441 490 gm
441 490 lin
441 488 gm
441 488 lin
441 491 gm
441 524 lin
441 527 gm
441 527 lin
441 525 gm
441 525 lin
442 80 gm
455 80 lin
442 82 gm
455 82 lin
458 80 gm
458 82 lin
456 80 gm
458 80 lin
456 82 gm
456 82 lin
456 82 lin
456 83 gm
456 131 lin
458 83 gm
458 131 lin
442 132 gm
455 132 lin
442 134 gm
455 134 lin
456 132 gm
456 134 lin
458 132 gm
458 134 lin
456 135 gm
456 182 lin
458 135 gm
458 182 lin
442 183 gm
455 183 lin
442 185 gm
455 185 lin
456 183 gm
456 185 lin
458 183 gm
458 185 lin
456 186 gm
456 253 lin
458 186 gm
458 253 lin
442 254 gm
455 254 lin
442 256 gm
455 256 lin
456 254 gm
456 256 lin
458 254 gm
458 256 lin
456 257 gm
456 290 lin
458 257 gm
458 290 lin
442 291 gm
455 291 lin
442 293 gm
455 293 lin
456 291 gm
456 293 lin
458 291 gm
458 293 lin
456 294 gm
456 327 lin
458 294 gm
458 327 lin
442 328 gm
455 328 lin
442 330 gm
455 330 lin
456 328 gm
456 330 lin
458 328 gm
458 330 lin
456 331 gm
456 364 lin
458 331 gm
458 364 lin
442 365 gm
455 365 lin
442 367 gm
455 367 lin
456 365 gm
456 367 lin
458 365 gm
458 367 lin
456 368 gm
456 400 lin
458 368 gm
458 400 lin
442 401 gm
455 401 lin
442 403 gm
455 403 lin
456 401 gm
456 403 lin
458 401 gm
458 403 lin
456 404 gm
456 487 lin
458 404 gm
458 487 lin
442 488 gm
455 488 lin
442 490 gm
455 490 lin
456 488 gm
456 490 lin
458 488 gm
458 490 lin
456 491 gm
456 524 lin
458 491 gm
458 524 lin
442 525 gm
455 525 lin
442 527 gm
455 527 lin
458 525 gm
458 527 lin
456 527 gm
458 527 lin
456 525 gm
456 525 lin
456 525 lin
470 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig.10)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Basic algorithm, iterative deepening and top-level sorting)show
486 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
1.85195 0. 32 0.18519 0.(The most impressive result in Fig.10 is the increasing of search overhead SO \(98% with 11)awidthshow
497 79 gm
0.59921 0. 32 0.05992 0.(processors\). The number of visited nodes is larger for 9 and 11 processors. On the other hand, the)awidthshow
508 79 gm
1.22573 0. 32 0.12257 0.(sequential version benefits from the new heuristics: the visited nodes are decreasd of 17%. We)awidthshow
519 79 gm
1.15554 0. 32 0.11555 0.(explain this with the fact that parallel search initially cannot gain any advantage from top level)awidthshow
530 79 gm
(sorting, since all processes start simultaneously with initial score equal to -)show
currentfont SwToSym
(\245)show
setfont
(.)show
541 79 gm
0.40695 0. 32 0.04069 0.(Moreover, with respect to no iterative deepening, in this case visited nodes include also all internal)awidthshow
552 79 gm
0.11657 0. 32 0.01165 0.(nodes: this explains the total count with 11 processors. However, the average production factor Fpm)awidthshow
563 79 gm
(decreases of 2%: there is a larger synchronization overhead due to search in the internal tree.)show
593 79 gm
1 fs
12 fz
bu fc
2 F /|______Times-Bold fnt
bn
(4.2 Reducing the search overhead)show
606 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
(Search overhead is caused:)show
618 88 gm
(\245\312by lack of sharing of score during search;)show
631 88 gm
(\245\312initial score = -)show
currentfont SwToSym
(\245)show
setfont
( for the first N)show
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(w)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
( tasks \(N)show
631 277 gm
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(w)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
( = # explorers\).)show
643 79 gm
0.40771 0. 32 0.04077 0.(We try to overcome such problems introducing a tuple storing a global score that all local searches)awidthshow
654 79 gm
1.10519 0. 32 0.11051 0.(can query. The global score tuple that can be read at any moment, but we must be careful with)awidthshow
665 79 gm
1.13174 0. 32 0.11317 0.(reading such a tuple, because it may be a very expensive operation. Thus, we try to make only)awidthshow
676 79 gm
0.11413 0. 32 0.01141 0.("useful" readings: after each reading of the global score the explorer puts in the tuple space a private)awidthshow
687 79 gm
0.35781 0. 32 0.03578 0.(tuple. When a worker modifies the global score it removes all private tuples, so that they can know)awidthshow
699 79 gm
0.66818 0. 32 0.06681 0.(when an update was done. In C-Linda )awidthshow
bu fc
2 F /|______Courier fnt
bn
0.27516 0.(out)ashow
bu fc
2 F /|______Times-Roman fnt
bn
0.73806 0. 32 0.07380 0.( operations are local and inexpensive, whereas )awidthshow
bu fc
2 F /|______Courier fnt
bn
0.27517 0.(in)ashow
bu fc
2 F /|______Times-Roman fnt
bn
0.51879 0. 32 0.05187 0.( are)awidthshow
710 79 gm
0.23971 0. 32 0.02397 0.(based on broadcasting and are expensive. Deletion of private tuples is expensive as well, but it does)awidthshow
721 79 gm
(not happen frequently. Fig.11 shows the evaluation of such an algorithm.)show
F T cp
%%Page: ? 12
op
30 28 811 566 fr
0 0 xl
1 1 pen
0 0 gm
(nc 0 0 0 0 6 rc)kp
91 336 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0 fs
10 fz
bu fc
2 F /|______Helvetica fnt
bn
(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
773 514 gm
(10)show
124 96 gm
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Procs)show
124 145 gm
(T\312\(sec\))show
124 200 gm
(N\312\(nodes\))show
124 271 gm
(S)show
124 308 gm
(E)show
124 338 gm
(Fpm)show
124 378 gm
(SO)show
124 416 gm
(SS\312\(nodes/sec\))show
124 502 gm
(Sss)show
110 80 gm
0 gr
110 82 lin
110 80 gm
112 80 lin
112 82 gm
112 82 lin
112 82 lin
110 83 gm
110 131 lin
112 83 gm
112 131 lin
110 132 gm
110 134 lin
112 132 gm
112 134 lin
110 135 gm
110 182 lin
112 135 gm
112 182 lin
110 183 gm
110 185 lin
112 183 gm
112 185 lin
110 186 gm
110 253 lin
112 186 gm
112 253 lin
110 254 gm
110 256 lin
112 254 gm
112 256 lin
110 257 gm
110 290 lin
112 257 gm
112 290 lin
110 291 gm
110 293 lin
112 291 gm
112 293 lin
110 294 gm
110 327 lin
112 294 gm
112 327 lin
110 328 gm
110 330 lin
112 328 gm
112 330 lin
110 331 gm
110 364 lin
112 331 gm
112 364 lin
110 365 gm
110 367 lin
112 365 gm
112 367 lin
110 368 gm
110 400 lin
112 368 gm
112 400 lin
110 401 gm
110 403 lin
112 401 gm
112 403 lin
110 404 gm
110 487 lin
112 404 gm
112 487 lin
110 488 gm
110 490 lin
112 488 gm
112 490 lin
110 491 gm
110 524 lin
112 491 gm
112 524 lin
110 525 gm
110 527 lin
112 527 lin
112 525 gm
112 525 lin
112 525 lin
113 80 gm
126 80 lin
113 82 gm
126 82 lin
113 132 gm
126 132 lin
113 134 gm
126 134 lin
113 183 gm
126 183 lin
113 185 gm
126 185 lin
113 254 gm
126 254 lin
113 256 gm
126 256 lin
113 291 gm
126 291 lin
113 293 gm
126 293 lin
113 328 gm
126 328 lin
113 330 gm
126 330 lin
113 365 gm
126 365 lin
113 367 gm
126 367 lin
113 401 gm
126 401 lin
113 403 gm
126 403 lin
113 488 gm
126 488 lin
113 490 gm
126 490 lin
113 525 gm
126 525 lin
113 527 gm
126 527 lin
141 105 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
141 149 gm
(6740)show
141 203 gm
(4529971)show
141 269 gm
(---)show
141 306 gm
(---)show
141 343 gm
(---)show
141 380 gm
(---)show
141 439 gm
(672)show
141 503 gm
(---)show
127 82 gm
0 gr
129 82 lin
127 80 gm
129 80 lin
127 83 gm
127 131 lin
129 83 gm
129 131 lin
127 134 gm
127 134 lin
129 132 gm
129 132 lin
127 132 gm
127 132 lin
129 134 gm
129 134 lin
127 135 gm
127 182 lin
129 135 gm
129 182 lin
127 185 gm
127 185 lin
129 183 gm
129 183 lin
127 183 gm
127 183 lin
129 185 gm
129 185 lin
127 186 gm
127 253 lin
129 186 gm
129 253 lin
127 256 gm
127 256 lin
129 254 gm
129 254 lin
127 254 gm
127 254 lin
129 256 gm
129 256 lin
127 257 gm
127 290 lin
129 257 gm
129 290 lin
127 293 gm
127 293 lin
129 291 gm
129 291 lin
127 291 gm
127 291 lin
129 293 gm
129 293 lin
127 294 gm
127 327 lin
129 294 gm
129 327 lin
127 330 gm
127 330 lin
129 328 gm
129 328 lin
127 328 gm
127 328 lin
129 330 gm
129 330 lin
127 331 gm
127 364 lin
129 331 gm
129 364 lin
127 367 gm
127 367 lin
129 365 gm
129 365 lin
127 365 gm
127 365 lin
129 367 gm
129 367 lin
127 368 gm
127 400 lin
129 368 gm
129 400 lin
127 403 gm
127 403 lin
129 401 gm
129 401 lin
127 401 gm
127 401 lin
129 403 gm
129 403 lin
127 404 gm
127 487 lin
129 404 gm
129 487 lin
127 490 gm
127 490 lin
129 488 gm
129 488 lin
127 488 gm
127 488 lin
129 490 gm
129 490 lin
127 491 gm
127 524 lin
129 491 gm
129 524 lin
127 527 gm
129 527 lin
127 525 gm
129 525 lin
130 80 gm
143 80 lin
130 82 gm
143 82 lin
130 132 gm
143 132 lin
130 134 gm
143 134 lin
130 183 gm
143 183 lin
130 185 gm
143 185 lin
130 254 gm
143 254 lin
130 256 gm
143 256 lin
130 291 gm
143 291 lin
130 293 gm
143 293 lin
130 328 gm
143 328 lin
130 330 gm
143 330 lin
130 365 gm
143 365 lin
130 367 gm
143 367 lin
130 401 gm
143 401 lin
130 403 gm
143 403 lin
130 488 gm
143 488 lin
130 490 gm
143 490 lin
130 525 gm
143 525 lin
130 527 gm
143 527 lin
156 105 gm
F 1 setTxMode
(3)show
156 149 gm
(2689)show
156 203 gm
(4995937)show
156 265 gm
(2.51)show
156 302 gm
(0.84)show
156 339 gm
(0.94)show
156 376 gm
(0.10)show
156 436 gm
(1858)show
156 499 gm
(2.76)show
144 82 gm
0 gr
144 82 lin
144 80 gm
144 80 lin
144 83 gm
144 131 lin
144 134 gm
144 134 lin
144 132 gm
144 132 lin
144 135 gm
144 182 lin
144 185 gm
144 185 lin
144 183 gm
144 183 lin
144 186 gm
144 253 lin
144 256 gm
144 256 lin
144 254 gm
144 254 lin
144 257 gm
144 290 lin
144 293 gm
144 293 lin
144 291 gm
144 291 lin
144 294 gm
144 327 lin
144 330 gm
144 330 lin
144 328 gm
144 328 lin
144 331 gm
144 364 lin
144 367 gm
144 367 lin
144 365 gm
144 365 lin
144 368 gm
144 400 lin
144 403 gm
144 403 lin
144 401 gm
144 401 lin
144 404 gm
144 487 lin
144 490 gm
144 490 lin
144 488 gm
144 488 lin
144 491 gm
144 524 lin
144 527 gm
144 527 lin
144 525 gm
144 525 lin
145 80 gm
158 80 lin
145 82 gm
158 82 lin
145 132 gm
158 132 lin
145 134 gm
158 134 lin
145 183 gm
158 183 lin
145 185 gm
158 185 lin
145 254 gm
158 254 lin
145 256 gm
158 256 lin
145 291 gm
158 291 lin
145 293 gm
158 293 lin
145 328 gm
158 328 lin
145 330 gm
158 330 lin
145 365 gm
158 365 lin
145 367 gm
158 367 lin
145 401 gm
158 401 lin
145 403 gm
158 403 lin
145 488 gm
158 488 lin
145 490 gm
158 490 lin
145 525 gm
158 525 lin
145 527 gm
158 527 lin
171 105 gm
F 1 setTxMode
(5)show
171 149 gm
(1854)show
171 203 gm
(5346599)show
171 265 gm
(3.64)show
171 302 gm
(0.73)show
171 339 gm
(0.88)show
171 376 gm
(0.18)show
171 436 gm
(2884)show
171 499 gm
(4.29)show
159 82 gm
0 gr
159 82 lin
159 80 gm
159 80 lin
159 83 gm
159 131 lin
159 134 gm
159 134 lin
159 132 gm
159 132 lin
159 135 gm
159 182 lin
159 185 gm
159 185 lin
159 183 gm
159 183 lin
159 186 gm
159 253 lin
159 256 gm
159 256 lin
159 254 gm
159 254 lin
159 257 gm
159 290 lin
159 293 gm
159 293 lin
159 291 gm
159 291 lin
159 294 gm
159 327 lin
159 330 gm
159 330 lin
159 328 gm
159 328 lin
159 331 gm
159 364 lin
159 367 gm
159 367 lin
159 365 gm
159 365 lin
159 368 gm
159 400 lin
159 403 gm
159 403 lin
159 401 gm
159 401 lin
159 404 gm
159 487 lin
159 490 gm
159 490 lin
159 488 gm
159 488 lin
159 491 gm
159 524 lin
159 527 gm
159 527 lin
159 525 gm
159 525 lin
160 80 gm
173 80 lin
160 82 gm
173 82 lin
160 132 gm
173 132 lin
160 134 gm
173 134 lin
160 183 gm
173 183 lin
160 185 gm
173 185 lin
160 254 gm
173 254 lin
160 256 gm
173 256 lin
160 291 gm
173 291 lin
160 293 gm
173 293 lin
160 328 gm
173 328 lin
160 330 gm
173 330 lin
160 365 gm
173 365 lin
160 367 gm
173 367 lin
160 401 gm
173 401 lin
160 403 gm
173 403 lin
160 488 gm
173 488 lin
160 490 gm
173 490 lin
160 525 gm
173 525 lin
160 527 gm
173 527 lin
186 105 gm
F 1 setTxMode
(7)show
186 149 gm
(1485)show
186 203 gm
(5634915)show
186 265 gm
(4.54)show
186 302 gm
(0.65)show
186 339 gm
(0.81)show
186 376 gm
(0.24)show
186 436 gm
(3795)show
186 499 gm
(5.65)show
174 82 gm
0 gr
174 82 lin
174 80 gm
174 80 lin
174 83 gm
174 131 lin
174 134 gm
174 134 lin
174 132 gm
174 132 lin
174 135 gm
174 182 lin
174 185 gm
174 185 lin
174 183 gm
174 183 lin
174 186 gm
174 253 lin
174 256 gm
174 256 lin
174 254 gm
174 254 lin
174 257 gm
174 290 lin
174 293 gm
174 293 lin
174 291 gm
174 291 lin
174 294 gm
174 327 lin
174 330 gm
174 330 lin
174 328 gm
174 328 lin
174 331 gm
174 364 lin
174 367 gm
174 367 lin
174 365 gm
174 365 lin
174 368 gm
174 400 lin
174 403 gm
174 403 lin
174 401 gm
174 401 lin
174 404 gm
174 487 lin
174 490 gm
174 490 lin
174 488 gm
174 488 lin
174 491 gm
174 524 lin
174 527 gm
174 527 lin
174 525 gm
174 525 lin
175 80 gm
188 80 lin
175 82 gm
188 82 lin
175 132 gm
188 132 lin
175 134 gm
188 134 lin
175 183 gm
188 183 lin
175 185 gm
188 185 lin
175 254 gm
188 254 lin
175 256 gm
188 256 lin
175 291 gm
188 291 lin
175 293 gm
188 293 lin
175 328 gm
188 328 lin
175 330 gm
188 330 lin
175 365 gm
188 365 lin
175 367 gm
188 367 lin
175 401 gm
188 401 lin
175 403 gm
188 403 lin
175 488 gm
188 488 lin
175 490 gm
188 490 lin
175 525 gm
188 525 lin
175 527 gm
188 527 lin
201 105 gm
F 1 setTxMode
(9)show
201 149 gm
(1315)show
201 203 gm
(5936185)show
201 265 gm
(5.13)show
201 302 gm
(0.57)show
201 339 gm
(0.77)show
201 376 gm
(0.31)show
201 436 gm
(4514)show
201 499 gm
(6.72)show
189 82 gm
0 gr
189 82 lin
189 80 gm
189 80 lin
189 83 gm
189 131 lin
189 134 gm
189 134 lin
189 132 gm
189 132 lin
189 135 gm
189 182 lin
189 185 gm
189 185 lin
189 183 gm
189 183 lin
189 186 gm
189 253 lin
189 256 gm
189 256 lin
189 254 gm
189 254 lin
189 257 gm
189 290 lin
189 293 gm
189 293 lin
189 291 gm
189 291 lin
189 294 gm
189 327 lin
189 330 gm
189 330 lin
189 328 gm
189 328 lin
189 331 gm
189 364 lin
189 367 gm
189 367 lin
189 365 gm
189 365 lin
189 368 gm
189 400 lin
189 403 gm
189 403 lin
189 401 gm
189 401 lin
189 404 gm
189 487 lin
189 490 gm
189 490 lin
189 488 gm
189 488 lin
189 491 gm
189 524 lin
189 527 gm
189 527 lin
189 525 gm
189 525 lin
190 80 gm
203 80 lin
190 82 gm
203 82 lin
190 132 gm
203 132 lin
190 134 gm
203 134 lin
190 183 gm
203 183 lin
190 185 gm
203 185 lin
190 254 gm
203 254 lin
190 256 gm
203 256 lin
190 291 gm
203 291 lin
190 293 gm
203 293 lin
190 328 gm
203 328 lin
190 330 gm
203 330 lin
190 365 gm
203 365 lin
190 367 gm
203 367 lin
190 401 gm
203 401 lin
190 403 gm
203 403 lin
190 488 gm
203 488 lin
190 490 gm
203 490 lin
190 525 gm
203 525 lin
190 527 gm
203 527 lin
216 103 gm
F 1 setTxMode
(11)show
216 149 gm
(1280)show
216 203 gm
(6726213)show
216 265 gm
(5.27)show
216 302 gm
(0.48)show
216 339 gm
(0.74)show
216 376 gm
(0.48)show
216 436 gm
(5255)show
216 499 gm
(7.82)show
204 82 gm
0 gr
204 82 lin
204 80 gm
204 80 lin
204 83 gm
204 131 lin
204 134 gm
204 134 lin
204 132 gm
204 132 lin
204 135 gm
204 182 lin
204 185 gm
204 185 lin
204 183 gm
204 183 lin
204 186 gm
204 253 lin
204 256 gm
204 256 lin
204 254 gm
204 254 lin
204 257 gm
204 290 lin
204 293 gm
204 293 lin
204 291 gm
204 291 lin
204 294 gm
204 327 lin
204 330 gm
204 330 lin
204 328 gm
204 328 lin
204 331 gm
204 364 lin
204 367 gm
204 367 lin
204 365 gm
204 365 lin
204 368 gm
204 400 lin
204 403 gm
204 403 lin
204 401 gm
204 401 lin
204 404 gm
204 487 lin
204 490 gm
204 490 lin
204 488 gm
204 488 lin
204 491 gm
204 524 lin
204 527 gm
204 527 lin
204 525 gm
204 525 lin
205 80 gm
218 80 lin
205 82 gm
218 82 lin
221 80 gm
221 82 lin
219 80 gm
221 80 lin
219 82 gm
219 82 lin
219 82 lin
219 83 gm
219 131 lin
221 83 gm
221 131 lin
205 132 gm
218 132 lin
205 134 gm
218 134 lin
219 132 gm
219 134 lin
221 132 gm
221 134 lin
219 135 gm
219 182 lin
221 135 gm
221 182 lin
205 183 gm
218 183 lin
205 185 gm
218 185 lin
219 183 gm
219 185 lin
221 183 gm
221 185 lin
219 186 gm
219 253 lin
221 186 gm
221 253 lin
205 254 gm
218 254 lin
205 256 gm
218 256 lin
219 254 gm
219 256 lin
221 254 gm
221 256 lin
219 257 gm
219 290 lin
221 257 gm
221 290 lin
205 291 gm
218 291 lin
205 293 gm
218 293 lin
219 291 gm
219 293 lin
221 291 gm
221 293 lin
219 294 gm
219 327 lin
221 294 gm
221 327 lin
205 328 gm
218 328 lin
205 330 gm
218 330 lin
219 328 gm
219 330 lin
221 328 gm
221 330 lin
219 331 gm
219 364 lin
221 331 gm
221 364 lin
205 365 gm
218 365 lin
205 367 gm
218 367 lin
219 365 gm
219 367 lin
221 365 gm
221 367 lin
219 368 gm
219 400 lin
221 368 gm
221 400 lin
205 401 gm
218 401 lin
205 403 gm
218 403 lin
219 401 gm
219 403 lin
221 401 gm
221 403 lin
219 404 gm
219 487 lin
221 404 gm
221 487 lin
205 488 gm
218 488 lin
205 490 gm
218 490 lin
219 488 gm
219 490 lin
221 488 gm
221 490 lin
219 491 gm
219 524 lin
221 491 gm
221 524 lin
205 525 gm
218 525 lin
205 527 gm
218 527 lin
221 525 gm
221 527 lin
219 527 gm
221 527 lin
219 525 gm
219 525 lin
219 525 lin
233 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig.11)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Score sharing)show
249 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
1.28097 0. 32 0.12809 0.(This table shows that we have achieved the goal of reducing search overhead SO \(62% with 9)awidthshow
264 79 gm
0.64041 0. 32 0.06404 0.(processors\); the speedup with 11 processors was improved of 42% \(3.69 )awidthshow
bu fc
2 F /|______Symbol fnt
bn
0.38940 0.(\256)ashow
bu fc
2 F /|______Times-Roman fnt
bn
0.52368 0. 32 0.05236 0.( 5.27\). Values for F)awidthshow
264 511 gm
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(pm)show
276 79 gm
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.95855 0. 32 0.09585 0.(are approximated: they do not take in account overhead due to updating the local score. We can)awidthshow
287 79 gm
(evaluate such an overhead as follows:)show
298 79 gm
0.60348 0. 32 0.06034 0.(\245\312with P processors, let Fpmr be the real production factor and OC  due to score sharing; we have)awidthshow
309 79 gm
(that:)show
0 0 pen
359 337 gm
(nc 313 164 359 337 6 rc)kp
0 gr
359 337 lin
psb
currentpoint
pse
313 164 gm
313 164 lin
psb
30 dict begin
currentpoint 3 -1 roll sub neg 3 1 roll sub 5536 div 1472 3 -1 roll exch div scale currentpoint translate 64 52 translate
-18 523 moveto
/fs 0 def
/sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def
/f1 {findfont dup /cf exch def sf} def
/ns {cf sf} def
384 /Helvetica f1
(S) show
238 523 moveto
224 ns
(VR) show
663 523 moveto
384 /Symbol f1
(=) show
963 523 moveto
384 /Helvetica f1
(P) show
1269 523 moveto
384 /Symbol f1
(\327) show
1395 523 moveto
384 /Helvetica f1
(F) show
1629 523 moveto
224 ns
(pmr) show
2121 523 moveto
384 /Symbol f1
(\336) show
2581 523 moveto
384 /Helvetica f1
(F) show
2815 523 moveto
224 ns
(pmr) show
3305 523 moveto
384 ns
(=) show
3652 284 moveto
(S) show
3908 284 moveto
224 ns
(VR) show
3804 816 moveto
384 ns
(P) show
/thick 0 def
/th { dup setlinewidth /thick exch def } def
16 th 3638 424 moveto 603 0 rlineto stroke
-34 1313 moveto
(F) show
200 1313 moveto
224 ns
(pm) show
618 1313 moveto
384 /Symbol f1
(=) show
918 1313 moveto
384 /Helvetica f1
(F) show
1152 1313 moveto
224 ns
(pmr) show
1626 1313 moveto
384 /Symbol f1
(+) show
1914 1313 moveto
384 /Helvetica f1
(OC) show
2582 1313 moveto
384 /Symbol f1
(\336) show
3062 1313 moveto
384 /Helvetica f1
(OC) show
3728 1313 moveto
(=) show
4027 1313 moveto
(F) show
4261 1313 moveto
224 ns
(pm) show
4634 1313 moveto
384 ns
(-) show
4805 1313 moveto
(F) show
5039 1313 moveto
224 ns
(pmr) show
end
pse
1 1 pen
368 79 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
(\245 in particular, with 11 processors:)show
0 0 pen
418 372 gm
(nc 372 164 418 372 6 rc)kp
0 gr
418 372 lin
psb
currentpoint
pse
372 164 gm
372 164 lin
psb
30 dict begin
currentpoint 3 -1 roll sub neg 3 1 roll sub 6656 div 1472 3 -1 roll exch div scale currentpoint translate 64 36 translate
-34 523 moveto
/fs 0 def
/sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def
/f1 {findfont dup /cf exch def sf} def
/ns {cf sf} def
384 /Helvetica f1
(F) show
200 523 moveto
224 ns
(pmr) show
601 523 moveto
384 /Helvetica f1
(\() show
721 523 moveto
384 /Helvetica f1
(11) show
1101 523 moveto
384 /Helvetica f1
(\)) show
1323 523 moveto
384 /Symbol f1
(=) show
1671 284 moveto
384 /Helvetica f1
(S) show
1927 284 moveto
224 ns
(VR) show
1823 816 moveto
384 ns
(P) show
/thick 0 def
/th { dup setlinewidth /thick exch def } def
16 th 1657 424 moveto 603 0 rlineto stroke
2384 523 moveto
384 /Symbol f1
(=) show
2733 284 moveto
384 /Helvetica f1
(7) show
2947 284 moveto
384 /Helvetica f1
(.) show
3086 284 moveto
384 /Helvetica f1
(82) show
2930 816 moveto
(11) show
2718 424 moveto 809 0 rlineto stroke
3651 523 moveto
384 /Symbol f1
(=) show
3969 523 moveto
384 /Helvetica f1
(0) show
4178 523 moveto
384 /Helvetica f1
(.) show
4314 523 moveto
384 /Helvetica f1
(71) show
-14 1313 moveto
384 /Helvetica f1
(OC) show
563 1313 moveto
384 /Helvetica f1
(\() show
683 1313 moveto
384 /Helvetica f1
(11) show
1063 1313 moveto
384 /Helvetica f1
(\)) show
1285 1313 moveto
384 /Symbol f1
(=) show
1585 1313 moveto
384 /Helvetica f1
(F) show
1819 1313 moveto
224 ns
(pm) show
2205 1313 moveto
384 /Symbol f1
(-) show
2472 1313 moveto
384 /Helvetica f1
(F) show
2706 1313 moveto
224 ns
(pmr) show
3211 1313 moveto
384 /Symbol f1
(=) show
3529 1313 moveto
384 /Helvetica f1
(0) show
3738 1313 moveto
384 /Helvetica f1
(.) show
3874 1313 moveto
384 /Helvetica f1
(74) show
4378 1313 moveto
384 /Symbol f1
(-) show
4663 1313 moveto
384 /Helvetica f1
(0) show
4872 1313 moveto
384 /Helvetica f1
(.) show
5008 1313 moveto
384 /Helvetica f1
(71) show
5478 1313 moveto
384 /Symbol f1
(=) show
5796 1313 moveto
384 /Helvetica f1
(0) show
6005 1313 moveto
384 /Helvetica f1
(.) show
6142 1313 moveto
384 /Helvetica f1
(03) show
end
pse
1 1 pen
427 79 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0.10513 0. 32 0.01051 0.(Communication overhead is not negligible, however the improvements in search overhead are worth)awidthshow
438 79 gm
(such a price.)show
468 79 gm
1 fs
12 fz
bu fc
2 F /|______Times-Bold fnt
bn
(4.3 PVSplit)show
481 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.94223 0. 32 0.09422 0.(We have tested PVSplit with iterative deepening \(INIT=2-plies and MAX=5-plies\) and top-level)awidthshow
492 79 gm
0.78674 0. 32 0.07867 0.(sorting; moreover, THRESOLD=3-plies. We have made two sets of experiments, with or without)awidthshow
503 79 gm
(global score.)show
532 96 gm
1 fs
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(procs)show
532 145 gm
(T\312\(sec\))show
532 200 gm
(N\312\(nodes\))show
532 271 gm
(S)show
532 308 gm
(E)show
532 338 gm
(Fpm)show
532 378 gm
(SO)show
532 416 gm
(SS\312\(nodes/sec\))show
532 502 gm
(Sss)show
518 80 gm
0 gr
518 82 lin
518 80 gm
520 80 lin
520 82 gm
520 82 lin
520 82 lin
518 83 gm
518 131 lin
520 83 gm
520 131 lin
518 132 gm
518 134 lin
520 132 gm
520 134 lin
518 135 gm
518 182 lin
520 135 gm
520 182 lin
518 183 gm
518 185 lin
520 183 gm
520 185 lin
518 186 gm
518 253 lin
520 186 gm
520 253 lin
518 254 gm
518 256 lin
520 254 gm
520 256 lin
518 257 gm
518 290 lin
520 257 gm
520 290 lin
518 291 gm
518 293 lin
520 291 gm
520 293 lin
518 294 gm
518 327 lin
520 294 gm
520 327 lin
518 328 gm
518 330 lin
520 328 gm
520 330 lin
518 331 gm
518 364 lin
520 331 gm
520 364 lin
518 365 gm
518 367 lin
520 365 gm
520 367 lin
518 368 gm
518 400 lin
520 368 gm
520 400 lin
518 401 gm
518 403 lin
520 401 gm
520 403 lin
518 404 gm
518 487 lin
520 404 gm
520 487 lin
518 488 gm
518 490 lin
520 488 gm
520 490 lin
518 491 gm
518 524 lin
520 491 gm
520 524 lin
518 525 gm
518 527 lin
520 527 lin
520 525 gm
520 525 lin
520 525 lin
521 80 gm
534 80 lin
521 82 gm
534 82 lin
521 132 gm
534 132 lin
521 134 gm
534 134 lin
521 183 gm
534 183 lin
521 185 gm
534 185 lin
521 254 gm
534 254 lin
521 256 gm
534 256 lin
521 291 gm
534 291 lin
521 293 gm
534 293 lin
521 328 gm
534 328 lin
521 330 gm
534 330 lin
521 365 gm
534 365 lin
521 367 gm
534 367 lin
521 401 gm
534 401 lin
521 403 gm
534 403 lin
521 488 gm
534 488 lin
521 490 gm
534 490 lin
521 525 gm
534 525 lin
521 527 gm
534 527 lin
549 105 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
549 149 gm
(6740)show
549 203 gm
(4529971)show
549 269 gm
(---)show
549 306 gm
(---)show
549 343 gm
(---)show
549 380 gm
(---)show
549 439 gm
(672)show
549 503 gm
(---)show
535 82 gm
0 gr
537 82 lin
535 80 gm
537 80 lin
535 83 gm
535 131 lin
537 83 gm
537 131 lin
535 134 gm
535 134 lin
537 132 gm
537 132 lin
535 132 gm
535 132 lin
537 134 gm
537 134 lin
535 135 gm
535 182 lin
537 135 gm
537 182 lin
535 185 gm
535 185 lin
537 183 gm
537 183 lin
535 183 gm
535 183 lin
537 185 gm
537 185 lin
535 186 gm
535 253 lin
537 186 gm
537 253 lin
535 256 gm
535 256 lin
537 254 gm
537 254 lin
535 254 gm
535 254 lin
537 256 gm
537 256 lin
535 257 gm
535 290 lin
537 257 gm
537 290 lin
535 293 gm
535 293 lin
537 291 gm
537 291 lin
535 291 gm
535 291 lin
537 293 gm
537 293 lin
535 294 gm
535 327 lin
537 294 gm
537 327 lin
535 330 gm
535 330 lin
537 328 gm
537 328 lin
535 328 gm
535 328 lin
537 330 gm
537 330 lin
535 331 gm
535 364 lin
537 331 gm
537 364 lin
535 367 gm
535 367 lin
537 365 gm
537 365 lin
535 365 gm
535 365 lin
537 367 gm
537 367 lin
535 368 gm
535 400 lin
537 368 gm
537 400 lin
535 403 gm
535 403 lin
537 401 gm
537 401 lin
535 401 gm
535 401 lin
537 403 gm
537 403 lin
535 404 gm
535 487 lin
537 404 gm
537 487 lin
535 490 gm
535 490 lin
537 488 gm
537 488 lin
535 488 gm
535 488 lin
537 490 gm
537 490 lin
535 491 gm
535 524 lin
537 491 gm
537 524 lin
535 527 gm
537 527 lin
535 525 gm
537 525 lin
538 80 gm
551 80 lin
538 82 gm
551 82 lin
538 132 gm
551 132 lin
538 134 gm
551 134 lin
538 183 gm
551 183 lin
538 185 gm
551 185 lin
538 254 gm
551 254 lin
538 256 gm
551 256 lin
538 291 gm
551 291 lin
538 293 gm
551 293 lin
538 328 gm
551 328 lin
538 330 gm
551 330 lin
538 365 gm
551 365 lin
538 367 gm
551 367 lin
538 401 gm
551 401 lin
538 403 gm
551 403 lin
538 488 gm
551 488 lin
538 490 gm
551 490 lin
538 525 gm
551 525 lin
538 527 gm
551 527 lin
564 105 gm
F 1 setTxMode
(3)show
564 149 gm
(2693)show
564 203 gm
(4949981)show
564 265 gm
(2.50)show
564 302 gm
(0.83)show
564 339 gm
(0.91)show
564 376 gm
(0.09)show
564 436 gm
(1838)show
564 499 gm
(2.73)show
552 82 gm
0 gr
552 82 lin
552 80 gm
552 80 lin
552 83 gm
552 131 lin
552 134 gm
552 134 lin
552 132 gm
552 132 lin
552 135 gm
552 182 lin
552 185 gm
552 185 lin
552 183 gm
552 183 lin
552 186 gm
552 253 lin
552 256 gm
552 256 lin
552 254 gm
552 254 lin
552 257 gm
552 290 lin
552 293 gm
552 293 lin
552 291 gm
552 291 lin
552 294 gm
552 327 lin
552 330 gm
552 330 lin
552 328 gm
552 328 lin
552 331 gm
552 364 lin
552 367 gm
552 367 lin
552 365 gm
552 365 lin
552 368 gm
552 400 lin
552 403 gm
552 403 lin
552 401 gm
552 401 lin
552 404 gm
552 487 lin
552 490 gm
552 490 lin
552 488 gm
552 488 lin
552 491 gm
552 524 lin
552 527 gm
552 527 lin
552 525 gm
552 525 lin
553 80 gm
566 80 lin
553 82 gm
566 82 lin
553 132 gm
566 132 lin
553 134 gm
566 134 lin
553 183 gm
566 183 lin
553 185 gm
566 185 lin
553 254 gm
566 254 lin
553 256 gm
566 256 lin
553 291 gm
566 291 lin
553 293 gm
566 293 lin
553 328 gm
566 328 lin
553 330 gm
566 330 lin
553 365 gm
566 365 lin
553 367 gm
566 367 lin
553 401 gm
566 401 lin
553 403 gm
566 403 lin
553 488 gm
566 488 lin
553 490 gm
566 490 lin
553 525 gm
566 525 lin
553 527 gm
566 527 lin
579 105 gm
F 1 setTxMode
(5)show
579 149 gm
(1931)show
579 203 gm
(5349308)show
579 265 gm
(3.49)show
579 302 gm
(0.70)show
579 339 gm
(0.82)show
579 376 gm
(0.18)show
579 436 gm
(2770)show
579 499 gm
(4.12)show
567 82 gm
0 gr
567 82 lin
567 80 gm
567 80 lin
567 83 gm
567 131 lin
567 134 gm
567 134 lin
567 132 gm
567 132 lin
567 135 gm
567 182 lin
567 185 gm
567 185 lin
567 183 gm
567 183 lin
567 186 gm
567 253 lin
567 256 gm
567 256 lin
567 254 gm
567 254 lin
567 257 gm
567 290 lin
567 293 gm
567 293 lin
567 291 gm
567 291 lin
567 294 gm
567 327 lin
567 330 gm
567 330 lin
567 328 gm
567 328 lin
567 331 gm
567 364 lin
567 367 gm
567 367 lin
567 365 gm
567 365 lin
567 368 gm
567 400 lin
567 403 gm
567 403 lin
567 401 gm
567 401 lin
567 404 gm
567 487 lin
567 490 gm
567 490 lin
567 488 gm
567 488 lin
567 491 gm
567 524 lin
567 527 gm
567 527 lin
567 525 gm
567 525 lin
568 80 gm
581 80 lin
568 82 gm
581 82 lin
568 132 gm
581 132 lin
568 134 gm
581 134 lin
568 183 gm
581 183 lin
568 185 gm
581 185 lin
568 254 gm
581 254 lin
568 256 gm
581 256 lin
568 291 gm
581 291 lin
568 293 gm
581 293 lin
568 328 gm
581 328 lin
568 330 gm
581 330 lin
568 365 gm
581 365 lin
568 367 gm
581 367 lin
568 401 gm
581 401 lin
568 403 gm
581 403 lin
568 488 gm
581 488 lin
568 490 gm
581 490 lin
568 525 gm
581 525 lin
568 527 gm
581 527 lin
594 105 gm
F 1 setTxMode
(7)show
594 149 gm
(1659)show
594 203 gm
(5657469)show
594 265 gm
(4.06)show
594 302 gm
(0.58)show
594 339 gm
(0.75)show
594 376 gm
(0.25)show
594 436 gm
(3410)show
594 499 gm
(5.07)show
582 82 gm
0 gr
582 82 lin
582 80 gm
582 80 lin
582 83 gm
582 131 lin
582 134 gm
582 134 lin
582 132 gm
582 132 lin
582 135 gm
582 182 lin
582 185 gm
582 185 lin
582 183 gm
582 183 lin
582 186 gm
582 253 lin
582 256 gm
582 256 lin
582 254 gm
582 254 lin
582 257 gm
582 290 lin
582 293 gm
582 293 lin
582 291 gm
582 291 lin
582 294 gm
582 327 lin
582 330 gm
582 330 lin
582 328 gm
582 328 lin
582 331 gm
582 364 lin
582 367 gm
582 367 lin
582 365 gm
582 365 lin
582 368 gm
582 400 lin
582 403 gm
582 403 lin
582 401 gm
582 401 lin
582 404 gm
582 487 lin
582 490 gm
582 490 lin
582 488 gm
582 488 lin
582 491 gm
582 524 lin
582 527 gm
582 527 lin
582 525 gm
582 525 lin
583 80 gm
596 80 lin
583 82 gm
596 82 lin
583 132 gm
596 132 lin
583 134 gm
596 134 lin
583 183 gm
596 183 lin
583 185 gm
596 185 lin
583 254 gm
596 254 lin
583 256 gm
596 256 lin
583 291 gm
596 291 lin
583 293 gm
596 293 lin
583 328 gm
596 328 lin
583 330 gm
596 330 lin
583 365 gm
596 365 lin
583 367 gm
596 367 lin
583 401 gm
596 401 lin
583 403 gm
596 403 lin
583 488 gm
596 488 lin
583 490 gm
596 490 lin
583 525 gm
596 525 lin
583 527 gm
596 527 lin
609 105 gm
F 1 setTxMode
(9)show
609 149 gm
(1502)show
609 203 gm
(6130143)show
609 265 gm
(4.49)show
609 302 gm
(0.50)show
609 339 gm
(0.67)show
609 376 gm
(0.35)show
609 436 gm
(4081)show
609 499 gm
(6.07)show
597 82 gm
0 gr
597 82 lin
597 80 gm
597 80 lin
597 83 gm
597 131 lin
597 134 gm
597 134 lin
597 132 gm
597 132 lin
597 135 gm
597 182 lin
597 185 gm
597 185 lin
597 183 gm
597 183 lin
597 186 gm
597 253 lin
597 256 gm
597 256 lin
597 254 gm
597 254 lin
597 257 gm
597 290 lin
597 293 gm
597 293 lin
597 291 gm
597 291 lin
597 294 gm
597 327 lin
597 330 gm
597 330 lin
597 328 gm
597 328 lin
597 331 gm
597 364 lin
597 367 gm
597 367 lin
597 365 gm
597 365 lin
597 368 gm
597 400 lin
597 403 gm
597 403 lin
597 401 gm
597 401 lin
597 404 gm
597 487 lin
597 490 gm
597 490 lin
597 488 gm
597 488 lin
597 491 gm
597 524 lin
597 527 gm
597 527 lin
597 525 gm
597 525 lin
598 80 gm
611 80 lin
598 82 gm
611 82 lin
598 132 gm
611 132 lin
598 134 gm
611 134 lin
598 183 gm
611 183 lin
598 185 gm
611 185 lin
598 254 gm
611 254 lin
598 256 gm
611 256 lin
598 291 gm
611 291 lin
598 293 gm
611 293 lin
598 328 gm
611 328 lin
598 330 gm
611 330 lin
598 365 gm
611 365 lin
598 367 gm
611 367 lin
598 401 gm
611 401 lin
598 403 gm
611 403 lin
598 488 gm
611 488 lin
598 490 gm
611 490 lin
598 525 gm
611 525 lin
598 527 gm
611 527 lin
624 103 gm
F 1 setTxMode
(11)show
624 149 gm
(1446)show
624 203 gm
(6445828)show
624 265 gm
(4.66)show
624 302 gm
(0.42)show
624 339 gm
(0.60)show
624 376 gm
(0.42)show
624 436 gm
(4458)show
624 499 gm
(6.63)show
612 82 gm
0 gr
612 82 lin
612 80 gm
612 80 lin
612 83 gm
612 131 lin
612 134 gm
612 134 lin
612 132 gm
612 132 lin
612 135 gm
612 182 lin
612 185 gm
612 185 lin
612 183 gm
612 183 lin
612 186 gm
612 253 lin
612 256 gm
612 256 lin
612 254 gm
612 254 lin
612 257 gm
612 290 lin
612 293 gm
612 293 lin
612 291 gm
612 291 lin
612 294 gm
612 327 lin
612 330 gm
612 330 lin
612 328 gm
612 328 lin
612 331 gm
612 364 lin
612 367 gm
612 367 lin
612 365 gm
612 365 lin
612 368 gm
612 400 lin
612 403 gm
612 403 lin
612 401 gm
612 401 lin
612 404 gm
612 487 lin
612 490 gm
612 490 lin
612 488 gm
612 488 lin
612 491 gm
612 524 lin
612 527 gm
612 527 lin
612 525 gm
612 525 lin
613 80 gm
626 80 lin
613 82 gm
626 82 lin
629 80 gm
629 82 lin
627 80 gm
629 80 lin
627 82 gm
627 82 lin
627 82 lin
627 83 gm
627 131 lin
629 83 gm
629 131 lin
613 132 gm
626 132 lin
613 134 gm
626 134 lin
627 132 gm
627 134 lin
629 132 gm
629 134 lin
627 135 gm
627 182 lin
629 135 gm
629 182 lin
613 183 gm
626 183 lin
613 185 gm
626 185 lin
627 183 gm
627 185 lin
629 183 gm
629 185 lin
627 186 gm
627 253 lin
629 186 gm
629 253 lin
613 254 gm
626 254 lin
613 256 gm
626 256 lin
627 254 gm
627 256 lin
629 254 gm
629 256 lin
627 257 gm
627 290 lin
629 257 gm
629 290 lin
613 291 gm
626 291 lin
613 293 gm
626 293 lin
627 291 gm
627 293 lin
629 291 gm
629 293 lin
627 294 gm
627 327 lin
629 294 gm
629 327 lin
613 328 gm
626 328 lin
613 330 gm
626 330 lin
627 328 gm
627 330 lin
629 328 gm
629 330 lin
627 331 gm
627 364 lin
629 331 gm
629 364 lin
613 365 gm
626 365 lin
613 367 gm
626 367 lin
627 365 gm
627 367 lin
629 365 gm
629 367 lin
627 368 gm
627 400 lin
629 368 gm
629 400 lin
613 401 gm
626 401 lin
613 403 gm
626 403 lin
627 401 gm
627 403 lin
629 401 gm
629 403 lin
627 404 gm
627 487 lin
629 404 gm
629 487 lin
613 488 gm
626 488 lin
613 490 gm
626 490 lin
627 488 gm
627 490 lin
629 488 gm
629 490 lin
627 491 gm
627 524 lin
629 491 gm
629 524 lin
613 525 gm
626 525 lin
613 527 gm
626 527 lin
629 525 gm
629 527 lin
627 527 gm
629 527 lin
627 525 gm
627 525 lin
627 525 lin
641 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig. 12 )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(PVSplit without score sharing)show
657 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.10940 0. 32 0.01094 0.(PVSplit reduces search overhead with respect to score sharing \(see Fig.11\), however its efficiency is)awidthshow
668 79 gm
0.78536 0. 32 0.07853 0.(lower. Compare the production factors: PVSplit gives very low values \(14% with 11 processors\).)awidthshow
679 79 gm
0.79605 0. 32 0.07960 0.(The reason is the synchronization necessary along the principal variation; we can reduce such an)awidthshow
690 79 gm
(overhead with a more balanced load distribution.)show
701 79 gm
0.02395 0. 32 0.00239 0.(We also have to take into account the fixed cost of each splitting: communication overhead has to be)awidthshow
712 79 gm
(multiplied for each node in the principal variation that is used for parallel splitting.)show
F T cp
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op
30 28 811 566 fr
0 0 xl
1 1 pen
0 0 gm
(nc 0 0 0 0 6 rc)kp
91 336 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0 fs
10 fz
bu fc
2 F /|______Helvetica fnt
bn
(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
773 514 gm
(11)show
124 96 gm
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Procs)show
124 145 gm
(T\312\(sec\))show
124 200 gm
(N\312\(nodes\))show
124 271 gm
(S)show
124 308 gm
(E)show
124 338 gm
(Fpm)show
124 378 gm
(SO)show
124 416 gm
(SS\312\(nodes/sec\))show
124 502 gm
(Sss)show
110 80 gm
0 gr
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112 364 lin
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112 400 lin
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112 487 lin
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112 491 gm
112 524 lin
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110 527 lin
112 527 lin
112 525 gm
112 525 lin
112 525 lin
113 80 gm
126 80 lin
113 82 gm
126 82 lin
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126 134 lin
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126 183 lin
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126 185 lin
113 254 gm
126 254 lin
113 256 gm
126 256 lin
113 291 gm
126 291 lin
113 293 gm
126 293 lin
113 328 gm
126 328 lin
113 330 gm
126 330 lin
113 365 gm
126 365 lin
113 367 gm
126 367 lin
113 401 gm
126 401 lin
113 403 gm
126 403 lin
113 488 gm
126 488 lin
113 490 gm
126 490 lin
113 525 gm
126 525 lin
113 527 gm
126 527 lin
141 105 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
141 149 gm
(6740)show
141 203 gm
(4529971)show
141 269 gm
(---)show
141 306 gm
(---)show
141 343 gm
(---)show
141 380 gm
(---)show
141 439 gm
(672)show
141 503 gm
(---)show
127 82 gm
0 gr
129 82 lin
127 80 gm
129 80 lin
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129 83 gm
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129 132 lin
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129 134 gm
129 134 lin
127 135 gm
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129 135 gm
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127 183 lin
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129 185 lin
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129 186 gm
129 253 lin
127 256 gm
127 256 lin
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129 254 lin
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127 254 lin
129 256 gm
129 256 lin
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127 290 lin
129 257 gm
129 290 lin
127 293 gm
127 293 lin
129 291 gm
129 291 lin
127 291 gm
127 291 lin
129 293 gm
129 293 lin
127 294 gm
127 327 lin
129 294 gm
129 327 lin
127 330 gm
127 330 lin
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129 328 lin
127 328 gm
127 328 lin
129 330 gm
129 330 lin
127 331 gm
127 364 lin
129 331 gm
129 364 lin
127 367 gm
127 367 lin
129 365 gm
129 365 lin
127 365 gm
127 365 lin
129 367 gm
129 367 lin
127 368 gm
127 400 lin
129 368 gm
129 400 lin
127 403 gm
127 403 lin
129 401 gm
129 401 lin
127 401 gm
127 401 lin
129 403 gm
129 403 lin
127 404 gm
127 487 lin
129 404 gm
129 487 lin
127 490 gm
127 490 lin
129 488 gm
129 488 lin
127 488 gm
127 488 lin
129 490 gm
129 490 lin
127 491 gm
127 524 lin
129 491 gm
129 524 lin
127 527 gm
129 527 lin
127 525 gm
129 525 lin
130 80 gm
143 80 lin
130 82 gm
143 82 lin
130 132 gm
143 132 lin
130 134 gm
143 134 lin
130 183 gm
143 183 lin
130 185 gm
143 185 lin
130 254 gm
143 254 lin
130 256 gm
143 256 lin
130 291 gm
143 291 lin
130 293 gm
143 293 lin
130 328 gm
143 328 lin
130 330 gm
143 330 lin
130 365 gm
143 365 lin
130 367 gm
143 367 lin
130 401 gm
143 401 lin
130 403 gm
143 403 lin
130 488 gm
143 488 lin
130 490 gm
143 490 lin
130 525 gm
143 525 lin
130 527 gm
143 527 lin
156 105 gm
F 1 setTxMode
(3)show
156 149 gm
(2640)show
156 203 gm
(4770665)show
156 265 gm
(2.55)show
156 302 gm
(0.85)show
156 339 gm
(0.91)show
156 376 gm
(0.05)show
156 436 gm
(1807)show
156 499 gm
(2.69)show
144 82 gm
0 gr
144 82 lin
144 80 gm
144 80 lin
144 83 gm
144 131 lin
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144 134 lin
144 132 gm
144 132 lin
144 135 gm
144 182 lin
144 185 gm
144 185 lin
144 183 gm
144 183 lin
144 186 gm
144 253 lin
144 256 gm
144 256 lin
144 254 gm
144 254 lin
144 257 gm
144 290 lin
144 293 gm
144 293 lin
144 291 gm
144 291 lin
144 294 gm
144 327 lin
144 330 gm
144 330 lin
144 328 gm
144 328 lin
144 331 gm
144 364 lin
144 367 gm
144 367 lin
144 365 gm
144 365 lin
144 368 gm
144 400 lin
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144 403 lin
144 401 gm
144 401 lin
144 404 gm
144 487 lin
144 490 gm
144 490 lin
144 488 gm
144 488 lin
144 491 gm
144 524 lin
144 527 gm
144 527 lin
144 525 gm
144 525 lin
145 80 gm
158 80 lin
145 82 gm
158 82 lin
145 132 gm
158 132 lin
145 134 gm
158 134 lin
145 183 gm
158 183 lin
145 185 gm
158 185 lin
145 254 gm
158 254 lin
145 256 gm
158 256 lin
145 291 gm
158 291 lin
145 293 gm
158 293 lin
145 328 gm
158 328 lin
145 330 gm
158 330 lin
145 365 gm
158 365 lin
145 367 gm
158 367 lin
145 401 gm
158 401 lin
145 403 gm
158 403 lin
145 488 gm
158 488 lin
145 490 gm
158 490 lin
145 525 gm
158 525 lin
145 527 gm
158 527 lin
171 105 gm
F 1 setTxMode
(5)show
171 149 gm
(1797)show
171 203 gm
(5020905)show
171 265 gm
(3.75)show
171 302 gm
(0.75)show
171 339 gm
(0.84)show
171 376 gm
(0.11)show
171 436 gm
(2794)show
171 499 gm
(4.16)show
159 82 gm
0 gr
159 82 lin
159 80 gm
159 80 lin
159 83 gm
159 131 lin
159 134 gm
159 134 lin
159 132 gm
159 132 lin
159 135 gm
159 182 lin
159 185 gm
159 185 lin
159 183 gm
159 183 lin
159 186 gm
159 253 lin
159 256 gm
159 256 lin
159 254 gm
159 254 lin
159 257 gm
159 290 lin
159 293 gm
159 293 lin
159 291 gm
159 291 lin
159 294 gm
159 327 lin
159 330 gm
159 330 lin
159 328 gm
159 328 lin
159 331 gm
159 364 lin
159 367 gm
159 367 lin
159 365 gm
159 365 lin
159 368 gm
159 400 lin
159 403 gm
159 403 lin
159 401 gm
159 401 lin
159 404 gm
159 487 lin
159 490 gm
159 490 lin
159 488 gm
159 488 lin
159 491 gm
159 524 lin
159 527 gm
159 527 lin
159 525 gm
159 525 lin
160 80 gm
173 80 lin
160 82 gm
173 82 lin
160 132 gm
173 132 lin
160 134 gm
173 134 lin
160 183 gm
173 183 lin
160 185 gm
173 185 lin
160 254 gm
173 254 lin
160 256 gm
173 256 lin
160 291 gm
173 291 lin
160 293 gm
173 293 lin
160 328 gm
173 328 lin
160 330 gm
173 330 lin
160 365 gm
173 365 lin
160 367 gm
173 367 lin
160 401 gm
173 401 lin
160 403 gm
173 403 lin
160 488 gm
173 488 lin
160 490 gm
173 490 lin
160 525 gm
173 525 lin
160 527 gm
173 527 lin
186 105 gm
F 1 setTxMode
(7)show
186 149 gm
(1443)show
186 203 gm
(5228542)show
186 265 gm
(4.67)show
186 302 gm
(0.67)show
186 339 gm
(0.77)show
186 376 gm
(0.15)show
186 436 gm
(3623)show
186 499 gm
(5.39)show
174 82 gm
0 gr
174 82 lin
174 80 gm
174 80 lin
174 83 gm
174 131 lin
174 134 gm
174 134 lin
174 132 gm
174 132 lin
174 135 gm
174 182 lin
174 185 gm
174 185 lin
174 183 gm
174 183 lin
174 186 gm
174 253 lin
174 256 gm
174 256 lin
174 254 gm
174 254 lin
174 257 gm
174 290 lin
174 293 gm
174 293 lin
174 291 gm
174 291 lin
174 294 gm
174 327 lin
174 330 gm
174 330 lin
174 328 gm
174 328 lin
174 331 gm
174 364 lin
174 367 gm
174 367 lin
174 365 gm
174 365 lin
174 368 gm
174 400 lin
174 403 gm
174 403 lin
174 401 gm
174 401 lin
174 404 gm
174 487 lin
174 490 gm
174 490 lin
174 488 gm
174 488 lin
174 491 gm
174 524 lin
174 527 gm
174 527 lin
174 525 gm
174 525 lin
175 80 gm
188 80 lin
175 82 gm
188 82 lin
175 132 gm
188 132 lin
175 134 gm
188 134 lin
175 183 gm
188 183 lin
175 185 gm
188 185 lin
175 254 gm
188 254 lin
175 256 gm
188 256 lin
175 291 gm
188 291 lin
175 293 gm
188 293 lin
175 328 gm
188 328 lin
175 330 gm
188 330 lin
175 365 gm
188 365 lin
175 367 gm
188 367 lin
175 401 gm
188 401 lin
175 403 gm
188 403 lin
175 488 gm
188 488 lin
175 490 gm
188 490 lin
175 525 gm
188 525 lin
175 527 gm
188 527 lin
201 105 gm
F 1 setTxMode
(9)show
201 149 gm
(1255)show
201 203 gm
(5358664)show
201 265 gm
(5.37)show
201 302 gm
(0.60)show
201 339 gm
(0.71)show
201 376 gm
(0.18)show
201 436 gm
(4270)show
201 499 gm
(6.35)show
189 82 gm
0 gr
189 82 lin
189 80 gm
189 80 lin
189 83 gm
189 131 lin
189 134 gm
189 134 lin
189 132 gm
189 132 lin
189 135 gm
189 182 lin
189 185 gm
189 185 lin
189 183 gm
189 183 lin
189 186 gm
189 253 lin
189 256 gm
189 256 lin
189 254 gm
189 254 lin
189 257 gm
189 290 lin
189 293 gm
189 293 lin
189 291 gm
189 291 lin
189 294 gm
189 327 lin
189 330 gm
189 330 lin
189 328 gm
189 328 lin
189 331 gm
189 364 lin
189 367 gm
189 367 lin
189 365 gm
189 365 lin
189 368 gm
189 400 lin
189 403 gm
189 403 lin
189 401 gm
189 401 lin
189 404 gm
189 487 lin
189 490 gm
189 490 lin
189 488 gm
189 488 lin
189 491 gm
189 524 lin
189 527 gm
189 527 lin
189 525 gm
189 525 lin
190 80 gm
203 80 lin
190 82 gm
203 82 lin
190 132 gm
203 132 lin
190 134 gm
203 134 lin
190 183 gm
203 183 lin
190 185 gm
203 185 lin
190 254 gm
203 254 lin
190 256 gm
203 256 lin
190 291 gm
203 291 lin
190 293 gm
203 293 lin
190 328 gm
203 328 lin
190 330 gm
203 330 lin
190 365 gm
203 365 lin
190 367 gm
203 367 lin
190 401 gm
203 401 lin
190 403 gm
203 403 lin
190 488 gm
203 488 lin
190 490 gm
203 490 lin
190 525 gm
203 525 lin
190 527 gm
203 527 lin
216 103 gm
F 1 setTxMode
(11)show
216 149 gm
(1210)show
216 203 gm
(5704328)show
216 265 gm
(5.57)show
216 302 gm
(0.51)show
216 339 gm
(0.64)show
216 376 gm
(0.26)show
216 436 gm
(4714)show
216 499 gm
(7.01)show
204 82 gm
0 gr
204 82 lin
204 80 gm
204 80 lin
204 83 gm
204 131 lin
204 134 gm
204 134 lin
204 132 gm
204 132 lin
204 135 gm
204 182 lin
204 185 gm
204 185 lin
204 183 gm
204 183 lin
204 186 gm
204 253 lin
204 256 gm
204 256 lin
204 254 gm
204 254 lin
204 257 gm
204 290 lin
204 293 gm
204 293 lin
204 291 gm
204 291 lin
204 294 gm
204 327 lin
204 330 gm
204 330 lin
204 328 gm
204 328 lin
204 331 gm
204 364 lin
204 367 gm
204 367 lin
204 365 gm
204 365 lin
204 368 gm
204 400 lin
204 403 gm
204 403 lin
204 401 gm
204 401 lin
204 404 gm
204 487 lin
204 490 gm
204 490 lin
204 488 gm
204 488 lin
204 491 gm
204 524 lin
204 527 gm
204 527 lin
204 525 gm
204 525 lin
205 80 gm
218 80 lin
205 82 gm
218 82 lin
221 80 gm
221 82 lin
219 80 gm
221 80 lin
219 82 gm
219 82 lin
219 82 lin
219 83 gm
219 131 lin
221 83 gm
221 131 lin
205 132 gm
218 132 lin
205 134 gm
218 134 lin
219 132 gm
219 134 lin
221 132 gm
221 134 lin
219 135 gm
219 182 lin
221 135 gm
221 182 lin
205 183 gm
218 183 lin
205 185 gm
218 185 lin
219 183 gm
219 185 lin
221 183 gm
221 185 lin
219 186 gm
219 253 lin
221 186 gm
221 253 lin
205 254 gm
218 254 lin
205 256 gm
218 256 lin
219 254 gm
219 256 lin
221 254 gm
221 256 lin
219 257 gm
219 290 lin
221 257 gm
221 290 lin
205 291 gm
218 291 lin
205 293 gm
218 293 lin
219 291 gm
219 293 lin
221 291 gm
221 293 lin
219 294 gm
219 327 lin
221 294 gm
221 327 lin
205 328 gm
218 328 lin
205 330 gm
218 330 lin
219 328 gm
219 330 lin
221 328 gm
221 330 lin
219 331 gm
219 364 lin
221 331 gm
221 364 lin
205 365 gm
218 365 lin
205 367 gm
218 367 lin
219 365 gm
219 367 lin
221 365 gm
221 367 lin
219 368 gm
219 400 lin
221 368 gm
221 400 lin
205 401 gm
218 401 lin
205 403 gm
218 403 lin
219 401 gm
219 403 lin
221 401 gm
221 403 lin
219 404 gm
219 487 lin
221 404 gm
221 487 lin
205 488 gm
218 488 lin
205 490 gm
218 490 lin
219 488 gm
219 490 lin
221 488 gm
221 490 lin
219 491 gm
219 524 lin
221 491 gm
221 524 lin
205 525 gm
218 525 lin
205 527 gm
218 527 lin
221 525 gm
221 527 lin
219 527 gm
221 527 lin
219 525 gm
219 525 lin
219 525 lin
233 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig.13)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(PVSplit with score sharing)show
249 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.65200 0. 32 0.06520 0.(Applying score sharing to PVSplit we reduce search overhead without loss \(Fig.13\): in fact, these)awidthshow
260 79 gm
(heuristics handle different parts of the game tree:)show
272 88 gm
(\245\312PVSplit is used in search of subtrees 2..P \(if we use P processors\))show
285 88 gm
(\245\312score sharing is used for subtrees after the Pth subtree.)show
297 79 gm
0.34881 0. 32 0.03488 0.(This algorithm gives the best speedups among those we have tested. We remark that there is a high)awidthshow
308 79 gm
(synchronization overhead caused by nodes along the principal variation.)show
338 79 gm
1 fs
12 fz
bu fc
2 F /|______Times-Bold fnt
bn
(5. Dynamic splitting)show
351 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.84838 0. 32 0.08483 0.(The main problem with static splitting is load distribution. The master-worker model is based on)awidthshow
362 79 gm
0.72189 0. 32 0.07218 0.(sequential jobs that are perfomed without attempting to parallelize them and are assigned without)awidthshow
377 79 gm
1.80435 0. 32 0.18043 0.(estimating the computational costs. Since for parallel )awidthshow
377 337 gm
bu fc
2 F /|______Symbol fnt
bn
0.74351 0.(ab)ashow
bu fc
2 F /|______Times-Roman fnt
bn
1.89697 0. 32 0.18969 0.( we cannot schedule jobs aiming at)awidthshow
389 79 gm
(minimizing idle times, there is no way of dynamically balancing the load.)show
419 79 gm
1 fs
12 fz
bu fc
2 F /|______Times-Bold fnt
bn
(5.1 Dynamic job allocation)show
432 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.39657 0. 32 0.03965 0.(A first solution to this problem consists of avoiding \322atomic\323 sequential jobs. We defined a variant)awidthshow
443 79 gm
0.75973 0. 32 0.07597 0.(of the core algorithm in which when there are no more jobs in the agenda the workers that finish)awidthshow
454 79 gm
0.38314 0. 32 0.03831 0.(their jobs help the busy ones. This means that a busy worker accepts help and splits its search tree,)awidthshow
465 79 gm
0.56610 0. 32 0.05661 0.(becoming a supervisor. We will apply this idea only to children of the root node. Since we cannot)awidthshow
476 79 gm
0.63034 0. 32 0.06303 0.(forecast how long the evaluation of a subtree will take, nor which nodes will be assigned to other)awidthshow
487 79 gm
(processors, we classify this a dynamic splitting algorithm.)show
498 79 gm
1.57165 0. 32 0.15716 0.(There are several choice to implement cooperation among workers: we have implemented the)awidthshow
509 79 gm
(following one.)show
521 88 gm
1.35116 0. 32 0.13511 0.(\245\312An explorer E)awidthshow
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.20555 0.(f)ashow
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
1.13021 0. 32 0.11302 0.( completes a search job and finds an empty agenda; however, there are other)awidthshow
532 101 gm
(workers still busy. E)show
532 191 gm
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(f)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
( notifies to be free to a busy worker E)show
532 359 gm
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(r)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
( ;)show
545 88 gm
(\245\312E)show
545 101 gm
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(r)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
( decomposes its subtree S, and sends tasks to free explorers;)show
557 79 gm
(Processes that cooperate to the search are dynamically partitioned in three sets:)show
569 88 gm
(\245\312set F of processes that completed their tasks and become free;)show
582 88 gm
(\245\312set R)show
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(p)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
( of processes that distribute their subtrees;)show
595 88 gm
(\245\312set R)show
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(s)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
( of processes that sequentially evaluate their subtrees.)show
F T cp
%%Page: ? 14
op
30 28 811 566 fr
0 0 xl
1 1 pen
0 0 gm
(nc 0 0 0 0 6 rc)kp
91 336 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0 fs
10 fz
bu fc
2 F /|______Helvetica fnt
bn
(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
773 514 gm
(12)show
781 538 734 505 th
158 243 gm
tu
(nc 110 104 505 499 6 rc)kp
ts
9 fz
bu fc
2 F /|______Helvetica fnt
bn
(P1)show
tu
ts
157 270 gm
(P2)show
tu
ts
158 297 gm
(P3)show
tu
ts
158 322 gm
(P4)show
tu
0 gr
146.5 238.5 163.5 256.5 0 rc
146.5 266.5 163.5 284.5 0 rc
146.5 293.5 163.5 310.5 0 rc
146.5 318.5 163.5 335.5 0 rc
ts
238 253 gm
F 1 setTxMode
(P1)show
tu
ts
237 279 gm
(P2)show
tu
ts
238 306 gm
(P4)show
tu
ts
281 279 gm
(P3)show
tu
0 gr
226.5 248.5 243.5 266.5 0 rc
226.5 275.5 243.5 293.5 0 rc
226.5 302.5 243.5 319.5 0 rc
269.5 275.5 286.5 292.5 0 rc
244 284 gm
269 284 lin
ts
346 260 gm
F 1 setTxMode
(P1)show
tu
ts
345 295 gm
(P4)show
tu
ts
391 258 gm
(P2)show
tu
0 gr
334.5 255.5 352.5 272.5 0 rc
334.5 291.5 351.5 309.5 0 rc
379.5 254.5 396.5 272.5 0 rc
ts
390 295 gm
F 1 setTxMode
(P3)show
tu
0 gr
378.5 291.5 396.5 308.5 0 rc
352 263 gm
378 263 lin
ts
147 361 gm
F 1 setTxMode
(Rs={P1,P2,P3,P4})show
157 361 gm
(Rp=)show
167 361 gm
(F=)show
tu
ts
250 372 gm
(Rs={P1,P4})show
260 372 gm
(Rp={P2})show
271 372 gm
(F={P3})show
tu
352 263 gm
0 gr
378 300 lin
ts
356 374 gm
F 1 setTxMode
(Rs={P4})show
367 374 gm
(Rp={P1})show
377 374 gm
(F={P2,P3})show
tu
ts
465 371 gm
(Rs=)show
475 371 gm
(Rp={P4})show
485 371 gm
(F={P1,P2,P3})show
tu
0 gr
136.5 358.5 174.5 431.5 0 rc
239.5 358.5 276.5 431.5 0 rc
347.5 358.5 385.5 431.5 0 rc
453.5 358.5 491.5 431.5 0 rc
ts
498 249 gm
F 1 setTxMode
(P1)show
tu
ts
497 276 gm
(P2)show
tu
ts
498 302 gm
(P3)show
tu
0 gr
486.5 245.5 503.5 262.5 0 rc
486.5 272.5 503.5 289.5 0 rc
486.5 299.5 503.5 316.5 0 rc
459 280 gm
486 280 lin
459 281 gm
486 308 lin
459 280 gm
486 253 lin
ts
453 276 gm
F 1 setTxMode
(P4)show
tu
0 gr
442.5 271.5 459.5 288.5 0 rc
pr
226 396 pl
216 392 pl
216 396 pl
216 398 pl
226 396 pl
4 ep
188 396 gm
216 396 lin
pr
332 396 pl
323 392 pl
323 396 pl
323 398 pl
332 396 pl
4 ep
295 396 gm
323 396 lin
pr
439 396 pl
430 392 pl
430 396 pl
430 398 pl
439 396 pl
4 ep
402 396 gm
430 396 lin
ts
246 108 gm
F 1 setTxMode
(democratic cooperation)show
257 108 gm
(at first level;)show
267 108 gm
(master-worker)show
277 108 gm
(with second level)show
tu
0 gr
427.5 106.5 443.5 216.5 0 rc
239.5 106.5 290.5 206.5 0 rc
164.5 110.5 180.5 214.5 0 rc
pr
159 229 pl
165 222 pl
162 221 pl
158 220 pl
159 229 pl
4 ep
164 212 gm
158 234 lin
pr
259 247 pl
264 238 pl
260 238 pl
258 237 pl
259 247 pl
4 ep
266 207 gm
260 238 lin
pr
332 242 pl
325 236 pl
323 238 pl
322 241 pl
332 242 pl
4 ep
265 207 gm
323 238 lin
pr
458 245 pl
454 236 pl
451 238 pl
449 239 pl
458 245 pl
4 ep
434 216 gm
451 238 lin
ts
175 112 gm
F 1 setTxMode
(democratic cooperation)show
tu
ts
465 386 gm
bu fc
2 F /|______Symbol fnt
bn
(\306)show
tu
ts
167 371 gm
(\306)show
tu
ts
158 377 gm
(\306)show
tu
ts
194 405 gm
bu fc
2 F /|______Helvetica fnt
bn
(P3 terminates a search)show
204 405 gm
(and informs P2;)show
214 405 gm
(P2 distributes a subtree)show
tu
ts
302 408 gm
(P2 terminates;)show
312 408 gm
(P1 distributes)show
323 408 gm
(two subtrees)show
tu
ts
410 405 gm
(P1 terminates;)show
420 405 gm
(P4 distributes)show
431 405 gm
(three subtrees)show
tu
ts
438 114 gm
(pure master-worker)show
tu
99 77 gm
(nc 30 28 811 566 6 rc)kp
0 gr
99 525 lin
544 244 gm
F 1 setTxMode
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
(Fig.14)show
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
( Dynamic splitting)show
562 77 gm
0 gr
562 525 lin
581 79 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
0.55099 0. 32 0.05509 0.(In this way we put a limit to the splittings that can happen at run-time, that are expensive: at most)awidthshow
592 79 gm
0.97015 0. 32 0.09701 0.(they are #F. Thus, the algorithm executed by each worker on its own subtree amounts to classic)awidthshow
603 79 gm
0.13885 0. 32 0.01388 0.(alphabeta until another worker declares to be available to help, after that the master-worker model is)awidthshow
614 79 gm
(used. The following table summarizes the results obtained with this algorithm.)show
643 96 gm
1 fs
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(Procs)show
643 145 gm
(T\312\(sec\))show
643 200 gm
(N\312\(nodes\))show
643 271 gm
(S)show
643 308 gm
(E)show
643 338 gm
(Fpm)show
643 378 gm
(SO)show
643 416 gm
(SS\312\(nodes/sec\))show
643 502 gm
(Sss)show
629 80 gm
0 gr
629 82 lin
629 80 gm
631 80 lin
631 82 gm
631 82 lin
631 82 lin
629 83 gm
629 131 lin
631 83 gm
631 131 lin
629 132 gm
629 134 lin
631 132 gm
631 134 lin
629 135 gm
629 182 lin
631 135 gm
631 182 lin
629 183 gm
629 185 lin
631 183 gm
631 185 lin
629 186 gm
629 253 lin
631 186 gm
631 253 lin
629 254 gm
629 256 lin
631 254 gm
631 256 lin
629 257 gm
629 290 lin
631 257 gm
631 290 lin
629 291 gm
629 293 lin
631 291 gm
631 293 lin
629 294 gm
629 327 lin
631 294 gm
631 327 lin
629 328 gm
629 330 lin
631 328 gm
631 330 lin
629 331 gm
629 364 lin
631 331 gm
631 364 lin
629 365 gm
629 367 lin
631 365 gm
631 367 lin
629 368 gm
629 400 lin
631 368 gm
631 400 lin
629 401 gm
629 403 lin
631 401 gm
631 403 lin
629 404 gm
629 487 lin
631 404 gm
631 487 lin
629 488 gm
629 490 lin
631 488 gm
631 490 lin
629 491 gm
629 524 lin
631 491 gm
631 524 lin
629 525 gm
629 527 lin
631 527 lin
631 525 gm
631 525 lin
631 525 lin
632 80 gm
645 80 lin
632 82 gm
645 82 lin
632 132 gm
645 132 lin
632 134 gm
645 134 lin
632 183 gm
645 183 lin
632 185 gm
645 185 lin
632 254 gm
645 254 lin
632 256 gm
645 256 lin
632 291 gm
645 291 lin
632 293 gm
645 293 lin
632 328 gm
645 328 lin
632 330 gm
645 330 lin
632 365 gm
645 365 lin
632 367 gm
645 367 lin
632 401 gm
645 401 lin
632 403 gm
645 403 lin
632 488 gm
645 488 lin
632 490 gm
645 490 lin
632 525 gm
645 525 lin
632 527 gm
645 527 lin
660 105 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
660 149 gm
(6740)show
660 203 gm
(4529971)show
660 269 gm
(---)show
660 306 gm
(---)show
660 343 gm
(---)show
660 380 gm
(---)show
660 439 gm
(672)show
660 503 gm
(---)show
646 82 gm
0 gr
648 82 lin
646 80 gm
648 80 lin
646 83 gm
646 131 lin
648 83 gm
648 131 lin
646 134 gm
646 134 lin
648 132 gm
648 132 lin
646 132 gm
646 132 lin
648 134 gm
648 134 lin
646 135 gm
646 182 lin
648 135 gm
648 182 lin
646 185 gm
646 185 lin
648 183 gm
648 183 lin
646 183 gm
646 183 lin
648 185 gm
648 185 lin
646 186 gm
646 253 lin
648 186 gm
648 253 lin
646 256 gm
646 256 lin
648 254 gm
648 254 lin
646 254 gm
646 254 lin
648 256 gm
648 256 lin
646 257 gm
646 290 lin
648 257 gm
648 290 lin
646 293 gm
646 293 lin
648 291 gm
648 291 lin
646 291 gm
646 291 lin
648 293 gm
648 293 lin
646 294 gm
646 327 lin
648 294 gm
648 327 lin
646 330 gm
646 330 lin
648 328 gm
648 328 lin
646 328 gm
646 328 lin
648 330 gm
648 330 lin
646 331 gm
646 364 lin
648 331 gm
648 364 lin
646 367 gm
646 367 lin
648 365 gm
648 365 lin
646 365 gm
646 365 lin
648 367 gm
648 367 lin
646 368 gm
646 400 lin
648 368 gm
648 400 lin
646 403 gm
646 403 lin
648 401 gm
648 401 lin
646 401 gm
646 401 lin
648 403 gm
648 403 lin
646 404 gm
646 487 lin
648 404 gm
648 487 lin
646 490 gm
646 490 lin
648 488 gm
648 488 lin
646 488 gm
646 488 lin
648 490 gm
648 490 lin
646 491 gm
646 524 lin
648 491 gm
648 524 lin
646 527 gm
648 527 lin
646 525 gm
648 525 lin
649 80 gm
662 80 lin
649 82 gm
662 82 lin
649 132 gm
662 132 lin
649 134 gm
662 134 lin
649 183 gm
662 183 lin
649 185 gm
662 185 lin
649 254 gm
662 254 lin
649 256 gm
662 256 lin
649 291 gm
662 291 lin
649 293 gm
662 293 lin
649 328 gm
662 328 lin
649 330 gm
662 330 lin
649 365 gm
662 365 lin
649 367 gm
662 367 lin
649 401 gm
662 401 lin
649 403 gm
662 403 lin
649 488 gm
662 488 lin
649 490 gm
662 490 lin
649 525 gm
662 525 lin
649 527 gm
662 527 lin
675 105 gm
F 1 setTxMode
(3)show
675 149 gm
(3019)show
675 203 gm
(5251659)show
675 265 gm
(2.23)show
675 302 gm
(0.74)show
675 339 gm
(0.93)show
675 376 gm
(0.16)show
675 436 gm
(1740)show
675 499 gm
(2.59)show
663 82 gm
0 gr
663 82 lin
663 80 gm
663 80 lin
663 83 gm
663 131 lin
663 134 gm
663 134 lin
663 132 gm
663 132 lin
663 135 gm
663 182 lin
663 185 gm
663 185 lin
663 183 gm
663 183 lin
663 186 gm
663 253 lin
663 256 gm
663 256 lin
663 254 gm
663 254 lin
663 257 gm
663 290 lin
663 293 gm
663 293 lin
663 291 gm
663 291 lin
663 294 gm
663 327 lin
663 330 gm
663 330 lin
663 328 gm
663 328 lin
663 331 gm
663 364 lin
663 367 gm
663 367 lin
663 365 gm
663 365 lin
663 368 gm
663 400 lin
663 403 gm
663 403 lin
663 401 gm
663 401 lin
663 404 gm
663 487 lin
663 490 gm
663 490 lin
663 488 gm
663 488 lin
663 491 gm
663 524 lin
663 527 gm
663 527 lin
663 525 gm
663 525 lin
664 80 gm
677 80 lin
664 82 gm
677 82 lin
664 132 gm
677 132 lin
664 134 gm
677 134 lin
664 183 gm
677 183 lin
664 185 gm
677 185 lin
664 254 gm
677 254 lin
664 256 gm
677 256 lin
664 291 gm
677 291 lin
664 293 gm
677 293 lin
664 328 gm
677 328 lin
664 330 gm
677 330 lin
664 365 gm
677 365 lin
664 367 gm
677 367 lin
664 401 gm
677 401 lin
664 403 gm
677 403 lin
664 488 gm
677 488 lin
664 490 gm
677 490 lin
664 525 gm
677 525 lin
664 527 gm
677 527 lin
690 105 gm
F 1 setTxMode
(5)show
690 149 gm
(2216)show
690 203 gm
(6322002)show
690 265 gm
(3.04)show
690 302 gm
(0.61)show
690 339 gm
(0.92)show
690 376 gm
(0.40)show
690 436 gm
(2853)show
690 499 gm
(4.24)show
678 82 gm
0 gr
678 82 lin
678 80 gm
678 80 lin
678 83 gm
678 131 lin
678 134 gm
678 134 lin
678 132 gm
678 132 lin
678 135 gm
678 182 lin
678 185 gm
678 185 lin
678 183 gm
678 183 lin
678 186 gm
678 253 lin
678 256 gm
678 256 lin
678 254 gm
678 254 lin
678 257 gm
678 290 lin
678 293 gm
678 293 lin
678 291 gm
678 291 lin
678 294 gm
678 327 lin
678 330 gm
678 330 lin
678 328 gm
678 328 lin
678 331 gm
678 364 lin
678 367 gm
678 367 lin
678 365 gm
678 365 lin
678 368 gm
678 400 lin
678 403 gm
678 403 lin
678 401 gm
678 401 lin
678 404 gm
678 487 lin
678 490 gm
678 490 lin
678 488 gm
678 488 lin
678 491 gm
678 524 lin
678 527 gm
678 527 lin
678 525 gm
678 525 lin
679 80 gm
692 80 lin
679 82 gm
692 82 lin
679 132 gm
692 132 lin
679 134 gm
692 134 lin
679 183 gm
692 183 lin
679 185 gm
692 185 lin
679 254 gm
692 254 lin
679 256 gm
692 256 lin
679 291 gm
692 291 lin
679 293 gm
692 293 lin
679 328 gm
692 328 lin
679 330 gm
692 330 lin
679 365 gm
692 365 lin
679 367 gm
692 367 lin
679 401 gm
692 401 lin
679 403 gm
692 403 lin
679 488 gm
692 488 lin
679 490 gm
692 490 lin
679 525 gm
692 525 lin
679 527 gm
692 527 lin
705 105 gm
F 1 setTxMode
(7)show
705 149 gm
(1921)show
705 203 gm
(7291629)show
705 265 gm
(3.51)show
705 302 gm
(0.50)show
705 339 gm
(0.91)show
705 376 gm
(0.61)show
705 436 gm
(3796)show
705 499 gm
(5.65)show
693 82 gm
0 gr
693 82 lin
693 80 gm
693 80 lin
693 83 gm
693 131 lin
693 134 gm
693 134 lin
693 132 gm
693 132 lin
693 135 gm
693 182 lin
693 185 gm
693 185 lin
693 183 gm
693 183 lin
693 186 gm
693 253 lin
693 256 gm
693 256 lin
693 254 gm
693 254 lin
693 257 gm
693 290 lin
693 293 gm
693 293 lin
693 291 gm
693 291 lin
693 294 gm
693 327 lin
693 330 gm
693 330 lin
693 328 gm
693 328 lin
693 331 gm
693 364 lin
693 367 gm
693 367 lin
693 365 gm
693 365 lin
693 368 gm
693 400 lin
693 403 gm
693 403 lin
693 401 gm
693 401 lin
693 404 gm
693 487 lin
693 490 gm
693 490 lin
693 488 gm
693 488 lin
693 491 gm
693 524 lin
693 527 gm
693 527 lin
693 525 gm
693 525 lin
694 80 gm
707 80 lin
694 82 gm
707 82 lin
694 132 gm
707 132 lin
694 134 gm
707 134 lin
694 183 gm
707 183 lin
694 185 gm
707 185 lin
694 254 gm
707 254 lin
694 256 gm
707 256 lin
694 291 gm
707 291 lin
694 293 gm
707 293 lin
694 328 gm
707 328 lin
694 330 gm
707 330 lin
694 365 gm
707 365 lin
694 367 gm
707 367 lin
694 401 gm
707 401 lin
694 403 gm
707 403 lin
694 488 gm
707 488 lin
694 490 gm
707 490 lin
694 525 gm
707 525 lin
694 527 gm
707 527 lin
720 105 gm
F 1 setTxMode
(9)show
720 149 gm
(1721)show
720 203 gm
(8300115)show
720 265 gm
(3.92)show
720 302 gm
(0.44)show
720 339 gm
(0.91)show
720 376 gm
(0.83)show
720 436 gm
(4823)show
720 499 gm
(7.18)show
708 82 gm
0 gr
708 82 lin
708 80 gm
708 80 lin
708 83 gm
708 131 lin
708 134 gm
708 134 lin
708 132 gm
708 132 lin
708 135 gm
708 182 lin
708 185 gm
708 185 lin
708 183 gm
708 183 lin
708 186 gm
708 253 lin
708 256 gm
708 256 lin
708 254 gm
708 254 lin
708 257 gm
708 290 lin
708 293 gm
708 293 lin
708 291 gm
708 291 lin
708 294 gm
708 327 lin
708 330 gm
708 330 lin
708 328 gm
708 328 lin
708 331 gm
708 364 lin
708 367 gm
708 367 lin
708 365 gm
708 365 lin
708 368 gm
708 400 lin
708 403 gm
708 403 lin
708 401 gm
708 401 lin
708 404 gm
708 487 lin
708 490 gm
708 490 lin
708 488 gm
708 488 lin
708 491 gm
708 524 lin
708 527 gm
708 527 lin
708 525 gm
708 525 lin
709 80 gm
722 80 lin
709 82 gm
722 82 lin
709 132 gm
722 132 lin
709 134 gm
722 134 lin
709 183 gm
722 183 lin
709 185 gm
722 185 lin
709 254 gm
722 254 lin
709 256 gm
722 256 lin
709 291 gm
722 291 lin
709 293 gm
722 293 lin
709 328 gm
722 328 lin
709 330 gm
722 330 lin
709 365 gm
722 365 lin
709 367 gm
722 367 lin
709 401 gm
722 401 lin
709 403 gm
722 403 lin
709 488 gm
722 488 lin
709 490 gm
722 490 lin
709 525 gm
722 525 lin
709 527 gm
722 527 lin
735 103 gm
F 1 setTxMode
(11)show
735 149 gm
(1600)show
735 203 gm
(9439299)show
735 265 gm
(4.21)show
735 302 gm
(0.38)show
735 339 gm
(0.90)show
735 376 gm
(1.08)show
735 436 gm
(5900)show
735 499 gm
(8.78)show
723 82 gm
0 gr
723 82 lin
723 80 gm
723 80 lin
723 83 gm
723 131 lin
723 134 gm
723 134 lin
723 132 gm
723 132 lin
723 135 gm
723 182 lin
723 185 gm
723 185 lin
723 183 gm
723 183 lin
723 186 gm
723 253 lin
723 256 gm
723 256 lin
723 254 gm
723 254 lin
723 257 gm
723 290 lin
723 293 gm
723 293 lin
723 291 gm
723 291 lin
723 294 gm
723 327 lin
723 330 gm
723 330 lin
723 328 gm
723 328 lin
723 331 gm
723 364 lin
723 367 gm
723 367 lin
723 365 gm
723 365 lin
723 368 gm
723 400 lin
723 403 gm
723 403 lin
723 401 gm
723 401 lin
723 404 gm
723 487 lin
723 490 gm
723 490 lin
723 488 gm
723 488 lin
723 491 gm
723 524 lin
723 527 gm
723 527 lin
723 525 gm
723 525 lin
724 80 gm
737 80 lin
724 82 gm
737 82 lin
740 80 gm
740 82 lin
738 80 gm
740 80 lin
738 82 gm
738 82 lin
738 82 lin
738 83 gm
738 131 lin
740 83 gm
740 131 lin
724 132 gm
737 132 lin
724 134 gm
737 134 lin
738 132 gm
738 134 lin
740 132 gm
740 134 lin
738 135 gm
738 182 lin
740 135 gm
740 182 lin
724 183 gm
737 183 lin
724 185 gm
737 185 lin
738 183 gm
738 185 lin
740 183 gm
740 185 lin
738 186 gm
738 253 lin
740 186 gm
740 253 lin
724 254 gm
737 254 lin
724 256 gm
737 256 lin
738 254 gm
738 256 lin
740 254 gm
740 256 lin
738 257 gm
738 290 lin
740 257 gm
740 290 lin
724 291 gm
737 291 lin
724 293 gm
737 293 lin
738 291 gm
738 293 lin
740 291 gm
740 293 lin
738 294 gm
738 327 lin
740 294 gm
740 327 lin
724 328 gm
737 328 lin
724 330 gm
737 330 lin
738 328 gm
738 330 lin
740 328 gm
740 330 lin
738 331 gm
738 364 lin
740 331 gm
740 364 lin
724 365 gm
737 365 lin
724 367 gm
737 367 lin
738 365 gm
738 367 lin
740 365 gm
740 367 lin
738 368 gm
738 400 lin
740 368 gm
740 400 lin
724 401 gm
737 401 lin
724 403 gm
737 403 lin
738 401 gm
738 403 lin
740 401 gm
740 403 lin
738 404 gm
738 487 lin
740 404 gm
740 487 lin
724 488 gm
737 488 lin
724 490 gm
737 490 lin
738 488 gm
738 490 lin
740 488 gm
740 490 lin
738 491 gm
738 524 lin
740 491 gm
740 524 lin
724 525 gm
737 525 lin
724 527 gm
737 527 lin
740 525 gm
740 527 lin
738 527 gm
740 527 lin
738 525 gm
738 525 lin
738 525 lin
752 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig.15)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Dynamic splitting of top level)show
F T cp
%%Page: ? 15
op
30 28 811 566 fr
0 0 xl
1 1 pen
0 0 gm
(nc 0 0 0 0 6 rc)kp
91 336 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0 fs
10 fz
bu fc
2 F /|______Helvetica fnt
bn
(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
773 514 gm
(13)show
122 79 gm
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
1.24938 0. 32 0.12493 0.(Compare this table with Fig.9. The average production factor is improved \(0.71)awidthshow
122 452 gm
bu fc
2 F /|______Symbol fnt
bn
0.69747 0.(\256)ashow
bu fc
2 F /|______Times-Roman fnt
bn
1.14624 0. 32 0.11462 0.(0.90 with 11)awidthshow
134 79 gm
1.77536 0. 32 0.17753 0.(processors\): this means that load balancing was better. More interestingly, such parameter is)awidthshow
145 79 gm
0.11734 0. 32 0.01173 0.(constant: the difference between 3 and 11 processors amounts only to 3%, so that there is little room)awidthshow
156 79 gm
0.57464 0. 32 0.05746 0.(to improve such values applying dynamic splitting also at lower levels of the game tree. Although)awidthshow
167 79 gm
0.54336 0. 32 0.05433 0.(search overhead is very high \(108% with 11 processors\), this waste does not overcome the gain in)awidthshow
178 79 gm
(synchronisation overhead.)show
189 79 gm
0.50170 0. 32 0.05017 0.(We have also tested a dynamic version of PVSplit, enriched with iterative deepening and top level)awidthshow
200 79 gm
(sorting; no global score is implemented \(Fig.16\).)show
229 96 gm
1 fs
10 fz
bu fc
2 F /|______Times-Bold fnt
bn
(Procs)show
229 145 gm
(T\312\(sec\))show
229 200 gm
(N\312\(nodes\))show
229 271 gm
(S)show
229 308 gm
(E)show
229 338 gm
(Fpm)show
229 378 gm
(SO)show
229 416 gm
(SS\312\(nodes/sec\))show
229 504 gm
(Ss)show
215 80 gm
0 gr
215 82 lin
215 80 gm
217 80 lin
217 82 gm
217 82 lin
217 82 lin
215 83 gm
215 131 lin
217 83 gm
217 131 lin
215 132 gm
215 134 lin
217 132 gm
217 134 lin
215 135 gm
215 182 lin
217 135 gm
217 182 lin
215 183 gm
215 185 lin
217 183 gm
217 185 lin
215 186 gm
215 253 lin
217 186 gm
217 253 lin
215 254 gm
215 256 lin
217 254 gm
217 256 lin
215 257 gm
215 290 lin
217 257 gm
217 290 lin
215 291 gm
215 293 lin
217 291 gm
217 293 lin
215 294 gm
215 327 lin
217 294 gm
217 327 lin
215 328 gm
215 330 lin
217 328 gm
217 330 lin
215 331 gm
215 364 lin
217 331 gm
217 364 lin
215 365 gm
215 367 lin
217 365 gm
217 367 lin
215 368 gm
215 400 lin
217 368 gm
217 400 lin
215 401 gm
215 403 lin
217 401 gm
217 403 lin
215 404 gm
215 487 lin
217 404 gm
217 487 lin
215 488 gm
215 490 lin
217 488 gm
217 490 lin
215 491 gm
215 524 lin
217 491 gm
217 524 lin
215 525 gm
215 527 lin
217 527 lin
217 525 gm
217 525 lin
217 525 lin
218 80 gm
231 80 lin
218 82 gm
231 82 lin
218 132 gm
231 132 lin
218 134 gm
231 134 lin
218 183 gm
231 183 lin
218 185 gm
231 185 lin
218 254 gm
231 254 lin
218 256 gm
231 256 lin
218 291 gm
231 291 lin
218 293 gm
231 293 lin
218 328 gm
231 328 lin
218 330 gm
231 330 lin
218 365 gm
231 365 lin
218 367 gm
231 367 lin
218 401 gm
231 401 lin
218 403 gm
231 403 lin
218 488 gm
231 488 lin
218 490 gm
231 490 lin
218 525 gm
231 525 lin
218 527 gm
231 527 lin
246 105 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
246 149 gm
(6740)show
246 203 gm
(4529971)show
246 269 gm
(---)show
246 306 gm
(---)show
246 343 gm
(---)show
246 380 gm
(---)show
246 439 gm
(672)show
246 503 gm
(---)show
232 82 gm
0 gr
234 82 lin
232 80 gm
234 80 lin
232 83 gm
232 131 lin
234 83 gm
234 131 lin
232 134 gm
232 134 lin
234 132 gm
234 132 lin
232 132 gm
232 132 lin
234 134 gm
234 134 lin
232 135 gm
232 182 lin
234 135 gm
234 182 lin
232 185 gm
232 185 lin
234 183 gm
234 183 lin
232 183 gm
232 183 lin
234 185 gm
234 185 lin
232 186 gm
232 253 lin
234 186 gm
234 253 lin
232 256 gm
232 256 lin
234 254 gm
234 254 lin
232 254 gm
232 254 lin
234 256 gm
234 256 lin
232 257 gm
232 290 lin
234 257 gm
234 290 lin
232 293 gm
232 293 lin
234 291 gm
234 291 lin
232 291 gm
232 291 lin
234 293 gm
234 293 lin
232 294 gm
232 327 lin
234 294 gm
234 327 lin
232 330 gm
232 330 lin
234 328 gm
234 328 lin
232 328 gm
232 328 lin
234 330 gm
234 330 lin
232 331 gm
232 364 lin
234 331 gm
234 364 lin
232 367 gm
232 367 lin
234 365 gm
234 365 lin
232 365 gm
232 365 lin
234 367 gm
234 367 lin
232 368 gm
232 400 lin
234 368 gm
234 400 lin
232 403 gm
232 403 lin
234 401 gm
234 401 lin
232 401 gm
232 401 lin
234 403 gm
234 403 lin
232 404 gm
232 487 lin
234 404 gm
234 487 lin
232 490 gm
232 490 lin
234 488 gm
234 488 lin
232 488 gm
232 488 lin
234 490 gm
234 490 lin
232 491 gm
232 524 lin
234 491 gm
234 524 lin
232 527 gm
234 527 lin
232 525 gm
234 525 lin
235 80 gm
248 80 lin
235 82 gm
248 82 lin
235 132 gm
248 132 lin
235 134 gm
248 134 lin
235 183 gm
248 183 lin
235 185 gm
248 185 lin
235 254 gm
248 254 lin
235 256 gm
248 256 lin
235 291 gm
248 291 lin
235 293 gm
248 293 lin
235 328 gm
248 328 lin
235 330 gm
248 330 lin
235 365 gm
248 365 lin
235 367 gm
248 367 lin
235 401 gm
248 401 lin
235 403 gm
248 403 lin
235 488 gm
248 488 lin
235 490 gm
248 490 lin
235 525 gm
248 525 lin
235 527 gm
248 527 lin
261 105 gm
F 1 setTxMode
(3)show
261 149 gm
(2532)show
261 203 gm
(4899016)show
261 265 gm
(2.66)show
261 302 gm
(0.89)show
261 339 gm
(0.90)show
261 376 gm
(0.08)show
261 436 gm
(1935)show
261 499 gm
(2.88)show
249 82 gm
0 gr
249 82 lin
249 80 gm
249 80 lin
249 83 gm
249 131 lin
249 134 gm
249 134 lin
249 132 gm
249 132 lin
249 135 gm
249 182 lin
249 185 gm
249 185 lin
249 183 gm
249 183 lin
249 186 gm
249 253 lin
249 256 gm
249 256 lin
249 254 gm
249 254 lin
249 257 gm
249 290 lin
249 293 gm
249 293 lin
249 291 gm
249 291 lin
249 294 gm
249 327 lin
249 330 gm
249 330 lin
249 328 gm
249 328 lin
249 331 gm
249 364 lin
249 367 gm
249 367 lin
249 365 gm
249 365 lin
249 368 gm
249 400 lin
249 403 gm
249 403 lin
249 401 gm
249 401 lin
249 404 gm
249 487 lin
249 490 gm
249 490 lin
249 488 gm
249 488 lin
249 491 gm
249 524 lin
249 527 gm
249 527 lin
249 525 gm
249 525 lin
250 80 gm
263 80 lin
250 82 gm
263 82 lin
250 132 gm
263 132 lin
250 134 gm
263 134 lin
250 183 gm
263 183 lin
250 185 gm
263 185 lin
250 254 gm
263 254 lin
250 256 gm
263 256 lin
250 291 gm
263 291 lin
250 293 gm
263 293 lin
250 328 gm
263 328 lin
250 330 gm
263 330 lin
250 365 gm
263 365 lin
250 367 gm
263 367 lin
250 401 gm
263 401 lin
250 403 gm
263 403 lin
250 488 gm
263 488 lin
250 490 gm
263 490 lin
250 525 gm
263 525 lin
250 527 gm
263 527 lin
276 105 gm
F 1 setTxMode
(5)show
276 149 gm
(1805)show
276 203 gm
(5453978)show
276 265 gm
(3.73)show
276 302 gm
(0.75)show
276 339 gm
(0.88)show
276 376 gm
(0.20)show
276 436 gm
(3022)show
276 499 gm
(4.50)show
264 82 gm
0 gr
264 82 lin
264 80 gm
264 80 lin
264 83 gm
264 131 lin
264 134 gm
264 134 lin
264 132 gm
264 132 lin
264 135 gm
264 182 lin
264 185 gm
264 185 lin
264 183 gm
264 183 lin
264 186 gm
264 253 lin
264 256 gm
264 256 lin
264 254 gm
264 254 lin
264 257 gm
264 290 lin
264 293 gm
264 293 lin
264 291 gm
264 291 lin
264 294 gm
264 327 lin
264 330 gm
264 330 lin
264 328 gm
264 328 lin
264 331 gm
264 364 lin
264 367 gm
264 367 lin
264 365 gm
264 365 lin
264 368 gm
264 400 lin
264 403 gm
264 403 lin
264 401 gm
264 401 lin
264 404 gm
264 487 lin
264 490 gm
264 490 lin
264 488 gm
264 488 lin
264 491 gm
264 524 lin
264 527 gm
264 527 lin
264 525 gm
264 525 lin
265 80 gm
278 80 lin
265 82 gm
278 82 lin
265 132 gm
278 132 lin
265 134 gm
278 134 lin
265 183 gm
278 183 lin
265 185 gm
278 185 lin
265 254 gm
278 254 lin
265 256 gm
278 256 lin
265 291 gm
278 291 lin
265 293 gm
278 293 lin
265 328 gm
278 328 lin
265 330 gm
278 330 lin
265 365 gm
278 365 lin
265 367 gm
278 367 lin
265 401 gm
278 401 lin
265 403 gm
278 403 lin
265 488 gm
278 488 lin
265 490 gm
278 490 lin
265 525 gm
278 525 lin
265 527 gm
278 527 lin
291 105 gm
F 1 setTxMode
(7)show
291 149 gm
(1486)show
291 203 gm
(5886412)show
291 265 gm
(4.54)show
291 302 gm
(0.65)show
291 339 gm
(0.87)show
291 376 gm
(0.30)show
291 436 gm
(3961)show
291 499 gm
(5.89)show
279 82 gm
0 gr
279 82 lin
279 80 gm
279 80 lin
279 83 gm
279 131 lin
279 134 gm
279 134 lin
279 132 gm
279 132 lin
279 135 gm
279 182 lin
279 185 gm
279 185 lin
279 183 gm
279 183 lin
279 186 gm
279 253 lin
279 256 gm
279 256 lin
279 254 gm
279 254 lin
279 257 gm
279 290 lin
279 293 gm
279 293 lin
279 291 gm
279 291 lin
279 294 gm
279 327 lin
279 330 gm
279 330 lin
279 328 gm
279 328 lin
279 331 gm
279 364 lin
279 367 gm
279 367 lin
279 365 gm
279 365 lin
279 368 gm
279 400 lin
279 403 gm
279 403 lin
279 401 gm
279 401 lin
279 404 gm
279 487 lin
279 490 gm
279 490 lin
279 488 gm
279 488 lin
279 491 gm
279 524 lin
279 527 gm
279 527 lin
279 525 gm
279 525 lin
280 80 gm
293 80 lin
280 82 gm
293 82 lin
280 132 gm
293 132 lin
280 134 gm
293 134 lin
280 183 gm
293 183 lin
280 185 gm
293 185 lin
280 254 gm
293 254 lin
280 256 gm
293 256 lin
280 291 gm
293 291 lin
280 293 gm
293 293 lin
280 328 gm
293 328 lin
280 330 gm
293 330 lin
280 365 gm
293 365 lin
280 367 gm
293 367 lin
280 401 gm
293 401 lin
280 403 gm
293 403 lin
280 488 gm
293 488 lin
280 490 gm
293 490 lin
280 525 gm
293 525 lin
280 527 gm
293 527 lin
306 105 gm
F 1 setTxMode
(9)show
306 149 gm
(1315)show
306 203 gm
(6386703)show
306 265 gm
(5.13)show
306 302 gm
(0.57)show
306 339 gm
(0.84)show
306 376 gm
(0.41)show
306 436 gm
(4857)show
306 499 gm
(7.23)show
294 82 gm
0 gr
294 82 lin
294 80 gm
294 80 lin
294 83 gm
294 131 lin
294 134 gm
294 134 lin
294 132 gm
294 132 lin
294 135 gm
294 182 lin
294 185 gm
294 185 lin
294 183 gm
294 183 lin
294 186 gm
294 253 lin
294 256 gm
294 256 lin
294 254 gm
294 254 lin
294 257 gm
294 290 lin
294 293 gm
294 293 lin
294 291 gm
294 291 lin
294 294 gm
294 327 lin
294 330 gm
294 330 lin
294 328 gm
294 328 lin
294 331 gm
294 364 lin
294 367 gm
294 367 lin
294 365 gm
294 365 lin
294 368 gm
294 400 lin
294 403 gm
294 403 lin
294 401 gm
294 401 lin
294 404 gm
294 487 lin
294 490 gm
294 490 lin
294 488 gm
294 488 lin
294 491 gm
294 524 lin
294 527 gm
294 527 lin
294 525 gm
294 525 lin
295 80 gm
308 80 lin
295 82 gm
308 82 lin
295 132 gm
308 132 lin
295 134 gm
308 134 lin
295 183 gm
308 183 lin
295 185 gm
308 185 lin
295 254 gm
308 254 lin
295 256 gm
308 256 lin
295 291 gm
308 291 lin
295 293 gm
308 293 lin
295 328 gm
308 328 lin
295 330 gm
308 330 lin
295 365 gm
308 365 lin
295 367 gm
308 367 lin
295 401 gm
308 401 lin
295 403 gm
308 403 lin
295 488 gm
308 488 lin
295 490 gm
308 490 lin
295 525 gm
308 525 lin
295 527 gm
308 527 lin
321 103 gm
F 1 setTxMode
(11)show
321 149 gm
(1208)show
321 203 gm
(6789922)show
321 265 gm
(5.58)show
321 302 gm
(0.51)show
321 339 gm
(0.80)show
321 376 gm
(0.50)show
321 436 gm
(5621)show
321 499 gm
(8.36)show
309 82 gm
0 gr
309 82 lin
309 80 gm
309 80 lin
309 83 gm
309 131 lin
309 134 gm
309 134 lin
309 132 gm
309 132 lin
309 135 gm
309 182 lin
309 185 gm
309 185 lin
309 183 gm
309 183 lin
309 186 gm
309 253 lin
309 256 gm
309 256 lin
309 254 gm
309 254 lin
309 257 gm
309 290 lin
309 293 gm
309 293 lin
309 291 gm
309 291 lin
309 294 gm
309 327 lin
309 330 gm
309 330 lin
309 328 gm
309 328 lin
309 331 gm
309 364 lin
309 367 gm
309 367 lin
309 365 gm
309 365 lin
309 368 gm
309 400 lin
309 403 gm
309 403 lin
309 401 gm
309 401 lin
309 404 gm
309 487 lin
309 490 gm
309 490 lin
309 488 gm
309 488 lin
309 491 gm
309 524 lin
309 527 gm
309 527 lin
309 525 gm
309 525 lin
310 80 gm
323 80 lin
310 82 gm
323 82 lin
326 80 gm
326 82 lin
324 80 gm
326 80 lin
324 82 gm
324 82 lin
324 82 lin
324 83 gm
324 131 lin
326 83 gm
326 131 lin
310 132 gm
323 132 lin
310 134 gm
323 134 lin
324 132 gm
324 134 lin
326 132 gm
326 134 lin
324 135 gm
324 182 lin
326 135 gm
326 182 lin
310 183 gm
323 183 lin
310 185 gm
323 185 lin
324 183 gm
324 185 lin
326 183 gm
326 185 lin
324 186 gm
324 253 lin
326 186 gm
326 253 lin
310 254 gm
323 254 lin
310 256 gm
323 256 lin
324 254 gm
324 256 lin
326 254 gm
326 256 lin
324 257 gm
324 290 lin
326 257 gm
326 290 lin
310 291 gm
323 291 lin
310 293 gm
323 293 lin
324 291 gm
324 293 lin
326 291 gm
326 293 lin
324 294 gm
324 327 lin
326 294 gm
326 327 lin
310 328 gm
323 328 lin
310 330 gm
323 330 lin
324 328 gm
324 330 lin
326 328 gm
326 330 lin
324 331 gm
324 364 lin
326 331 gm
326 364 lin
310 365 gm
323 365 lin
310 367 gm
323 367 lin
324 365 gm
324 367 lin
326 365 gm
326 367 lin
324 368 gm
324 400 lin
326 368 gm
326 400 lin
310 401 gm
323 401 lin
310 403 gm
323 403 lin
324 401 gm
324 403 lin
326 401 gm
326 403 lin
324 404 gm
324 487 lin
326 404 gm
326 487 lin
310 488 gm
323 488 lin
310 490 gm
323 490 lin
324 488 gm
324 490 lin
326 488 gm
326 490 lin
324 491 gm
324 524 lin
326 491 gm
326 524 lin
310 525 gm
323 525 lin
310 527 gm
323 527 lin
326 525 gm
326 527 lin
324 527 gm
326 527 lin
324 525 gm
324 525 lin
324 525 lin
338 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig.16)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Dynamic PVSplit)show
354 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.38436 0. 32 0.03843 0.(Search overhead is low, and efficiency is good: the speedup S with 11 processors was improved of)awidthshow
365 79 gm
(24% with respect to data shown in\312Fig.11.)show
395 79 gm
1 fs
12 fz
bu fc
2 F /|______Times-Bold fnt
bn
(5.2 A discussion of dynamic splitting)show
408 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.89706 0. 32 0.08970 0.(The algorithm described in Sect. 5.1 is not really representative of dynamic splitting methods. A)awidthshow
419 79 gm
(more general definition of such a concept should answer to the following questions:)show
431 88 gm
(\245\312when a supervisor process P visiting a node N should create a new parallel task?)show
444 88 gm
(\245\312who executes the task?)show
457 88 gm
(\245\312which data can be use to make a splitting decision?)show
469 79 gm
0.21591 0. 32 0.02159 0.(Consider the game tree in Fig.17; process P is responsible of its evaluation because it was given the)awidthshow
484 79 gm
0.60699 0. 32 0.06069 0.(root. According to the depth)awidthshow
484 207 gm
0.67794 0. 32 0.06779 0.(-first rule used in )awidthshow
484 289 gm
bu fc
2 F /|______Symbol fnt
bn
0.20346 0.(ab)ashow
bu fc
2 F /|______Times-Roman fnt
bn
0.57464 0. 32 0.05746 0.(, we have the following sequence for successors:)awidthshow
496 79 gm
(N)show
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
(, N)show
496 103 gm
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(2)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
(, N)show
496 120 gm
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(3)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
(.)show
(nc 520 237 675 366 6 rc)kp
0 gr
601.5 241.5 628.5 268.5 0 ov
601.5 285.5 628.5 312.5 0 ov
601.5 329.5 628.5 356.5 0 ov
522.5 285.5 548.5 312.5 0 ov
616 250 gm
(nc 608 249 619 261 6 rc)kp
F 1 setTxMode
9 fz
bu fc
2 F /|______Helvetica fnt
bn
(N)show
7 fz
bu fc
2 F /|______Helvetica fnt
bn
(1)show
617 295 gm
(nc 609 294 620 306 6 rc)kp
9 fz
bu fc
2 F /|______Helvetica fnt
bn
(N)show
7 fz
bu fc
2 F /|______Helvetica fnt
bn
(2)show
616 339 gm
(nc 608 338 619 350 6 rc)kp
9 fz
bu fc
2 F /|______Helvetica fnt
bn
(N)show
7 fz
bu fc
2 F /|______Helvetica fnt
bn
(3)show
538 316 gm
(nc 530 315 541 323 6 rc)kp
9 fz
bu fc
2 F /|______Helvetica fnt
bn
(P)show
601 299 gm
(nc 520 237 675 366 6 rc)kp
0 gr
548 299 lin
601 343 lin
0 0 2 9 6 2 dh
548 299 gm
601 255 lin
rh
psb
pse
0 0 2 9 6 2 dh
599 239 gm
628 271 lin
rh
psb
pse
0 0 2 9 6 2 dh
628 240 gm
595 268 lin
rh
psb
pse
617 359 gm
(nc 608 358 620 365 6 rc)kp
F 1 setTxMode
10 fz
bu fc
2 F /|______Helvetica fnt
bn
(?)show
616 315 gm
(nc 607 314 619 321 6 rc)kp
(?)show
628 299 gm
(nc 520 237 675 366 6 rc)kp
0 gr
673 282 lin
628 299 gm
673 311 lin
673 282 gm
673 311 lin
0 0 2 9 6 2 dh
628 255 gm
673 239 lin
rh
psb
pse
0 0 2 9 6 2 dh
628 255 gm
673 268 lin
rh
psb
pse
0 0 2 9 6 2 dh
673 239 gm
673 268 lin
rh
psb
pse
628 343 gm
673 326 lin
628 343 gm
673 355 lin
673 326 gm
673 355 lin
537 290 gm
(nc 529 289 540 310 6 rc)kp
F 1 setTxMode
9 fz
bu fc
2 F /|______Helvetica fnt
bn
(Root)show
509 77 gm
(nc 30 28 811 566 6 rc)kp
0 gr
509 525 lin
703 131 gm
F 1 setTxMode
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
(Fig.17)show
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
( Problems with dynamic splitting: who has to evaluate N2 and N3?)show
721 77 gm
0 gr
721 525 lin
740 79 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
0.05569 0. 32 0.00556 0.(Suppose the subtree with root N)awidthshow
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.04531 0. 32 0.00453 0.( has been evaluated; if no cuts were produced P has to start the visit)awidthshow
751 79 gm
0.49194 0. 32 0.04919 0.(of N)awidthshow
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.15614 0.(2)ashow
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.47515 0. 32 0.04751 0.(, i.e. it generates the task of visiting N)awidthshow
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.15614 0.(2)ashow
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.45867 0. 32 0.04586 0.(. It can happen that P itself is assigned to this task, so)awidthshow
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F 1 setTxMode
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(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
773 514 gm
(14)show
118 79 gm
11 fz
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0.66665 0. 32 0.06666 0.(that only when such a visit is completed N)awidthshow
118 274 gm
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0.20846 0.(3)ashow
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0.66177 0. 32 0.06617 0.( will be evaluated, unless a cut is produced. If P were)awidthshow
129 79 gm
0.21484 0. 32 0.02148 0.(assigned all successors of the root node shown in Fig.17, then actually no splitting would have been)awidthshow
140 79 gm
0.04959 0. 32 0.00495 0.(done in the root. Instead, suppose that N)awidthshow
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bu fc
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(2)show
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0.04257 0. 32 0.00425 0.( is given to a process Q different from P; then, P should not)awidthshow
151 79 gm
0.30273 0. 32 0.03027 0.(block itself waiting for Q, but should continue the visit and allocate a task for the evaluation of N)awidthshow
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0.08947 0.(3)ashow
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(.)show
162 79 gm
0.87707 0. 32 0.08770 0.(In this way we have a splitting only if this is really necessary; moreover, we improve control on)awidthshow
173 79 gm
(search overhead and load balancing.)show
184 79 gm
1.54342 0. 32 0.15434 0.(An important decision when using of this kind of algorithm is the knowledge necessary for a)awidthshow
195 79 gm
0.94299 0. 32 0.09429 0.(splitting. There are two kinds of knowledge that are necessary for a process P to take a splitting)awidthshow
206 79 gm
(decision on a node N:)show
218 88 gm
0.76568 0. 32 0.07656 0.(- local knowledge, )awidthshow
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0.15858 0.(i.e)ashow
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0.63476 0. 32 0.06347 0.(. data owned by the process P itself that is going to decide a splitting. For)awidthshow
229 101 gm
0.12954 0. 32 0.01295 0.(instance, knowledge on the level of N in the game tree, or on the size of the subtree whose root)awidthshow
240 101 gm
(is N, is local.)show
253 88 gm
0.03265 0. 32 0.00326 0.(- global knowledge, )awidthshow
253 178 gm
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(i.e)show
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0.02944 0. 32 0.00294 0.(. data that have to be asked to the operating environment. For instance, how)awidthshow
264 101 gm
1.16287 0. 32 0.11628 0.(many processors are idle or how many tasks are still in the agenda are examples of global)awidthshow
275 101 gm
(knowledge.)show
287 79 gm
0.30563 0. 32 0.03056 0.(Suppose that in order to decide if N is a splitting node we only use knowledge local to P, assigning)awidthshow
298 79 gm
0.62866 0. 32 0.06286 0.(N and its subtree to P itself: the decision will be very rapid. However, load balancing will rapidly)awidthshow
309 79 gm
0.19454 0. 32 0.01945 0.(deteriorate. Thus, we need to combine both form of knowledge; we achieve this taking a decision in)awidthshow
320 79 gm
(two steps:)show
332 88 gm
(i\)\312let P be the supervisor of N; we make a local test to see if P itself can take charge of N;)show
345 88 gm
0.44586 0. 32 0.04458 0.(ii\)\312if not, we use global knowledge to choose a different supervisor. This implies communicating)awidthshow
356 101 gm
(with other processes.)show
368 79 gm
1.46865 0. 32 0.14686 0.(We put all global data in tuples: both the task to be assigned to a worker, corresponding to a)awidthshow
379 79 gm
0.64743 0. 32 0.06474 0.(splitting, and data to make splitting decisions. A node N becomes a splitting node when search of)awidthshow
390 79 gm
0.07965 0. 32 0.00796 0.(one of its children is given to another process. A splitting decision needs data that can be either local)awidthshow
401 79 gm
0.11535 0. 32 0.01153 0.(or non-local. In general non-local data are more expensive to acquire, thus we classify splitting rules)awidthshow
412 79 gm
0.48583 0. 32 0.04858 0.(built in the Boolean function as local or global. Local rules say when it is not convenient to start a)awidthshow
423 79 gm
(parallel task; if local rules require splitting, then global data are acquired.)show
434 79 gm
(This is a very partial list of criteria based on local data:)show
446 88 gm
1.15356 0. 32 0.11535 0.(\245\312subtree size: small subtrees are not distributed. Subtree size should be measured in terms of)awidthshow
457 101 gm
0.61340 0. 32 0.06134 0.(nodes, but this figure is not known before the visit; however, it is possible to estimate such a)awidthshow
472 101 gm
0.11322 0. 32 0.01132 0.(quantity knowing the tree depth and the wideness of the initial )awidthshow
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0.14205 0. 32 0.01420 0.( window [Bau78]. A measure)awidthshow
484 101 gm
(simpler to obtain is given by the tree depth [Eli90].)show
497 88 gm
0.10589 0. 32 0.01058 0.(\245\312"young-brothers-wait" [FMMV89]: aims at reducing search overhead if the game tree is ordered.)awidthshow
508 101 gm
0.99380 0. 32 0.09938 0.(The first successor of a node has to be completely evaluated before proceeding in the visit.)awidthshow
519 101 gm
2.21588 0. 32 0.22158 0.(Thus a node N has to be evaluated by its supervisor if it is the first to be visited. A)awidthshow
530 101 gm
2.09609 0. 32 0.20960 0.(generalisation of this method consists of avoiding the distribution of the first K \(K>1\))awidthshow
541 101 gm
0.37506 0. 32 0.03750 0.(successors. For ordered game trees the best moves are with high probability "on the left", thus)awidthshow
556 101 gm
(if we give priority to this side we get better )show
556 293 gm
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( windows for continuing the search in parallel.)show
570 88 gm
1.08642 0. 32 0.10864 0.(\245\312limiting the max. number of children visited in parallel: the idea is to get a good amount of)awidthshow
581 101 gm
1.09680 0. 32 0.10968 0.(information from incomplete searches. The supervisor only need to know how many nodes)awidthshow
592 101 gm
(were distributed but  not yet entirely searched.)show
604 79 gm
(The following criteria are based on global knowledge:)show
616 88 gm
0.44174 0. 32 0.04417 0.(\245\312limiting the number of tasks in agenda, aiming at reducing synchronisation overhead. In fact, if)awidthshow
627 101 gm
1.18713 0. 32 0.11871 0.(tasks were too many with respect to the available processors, the task originators could be)awidthshow
638 101 gm
1.72622 0. 32 0.17262 0.(strongly slowed. A typical value that can be chosen as maximum is the total number of)awidthshow
649 101 gm
0.63552 0. 32 0.06355 0.(processors. We put a counter in a single tuple; the counter is incremented by supervisors and)awidthshow
660 101 gm
(decremented by workers.)show
673 88 gm
0.15594 0. 32 0.01559 0.(\245\312splitting only in case of idle processor: we avoid that a task remains too much time in agenda, so)awidthshow
684 101 gm
1.12258 0. 32 0.11225 0.(that we reduce synchronisation overhead. We need to count how many processors are idle,)awidthshow
695 101 gm
(again with a counter tuple.)show
707 79 gm
(Now we are ready to describe a dynamic algorithm parametric wrt the splitting rules.)show
737 79 gm
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(5.3 A general algorithm for dynamic splitting)show
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(A Comparison of Parallel Search Algorithms)show
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1.21017 0. 32 0.12101 0.(We have designed a software architecture that is easy to adapt to different splitting algorithms.)awidthshow
129 79 gm
0.08255 0. 32 0.00825 0.(Given a splitting criterion, we specialise the core algorithm aiming at maximising the efficiency. We)awidthshow
140 79 gm
0.30303 0. 32 0.03030 0.(note that we could treat most static splitting algorithms as special cases of trivial dynamic splitting,)awidthshow
151 79 gm
1.00021 0. 32 0.10002 0.(however we would lose most of the optimisations that were possible because the splitting nodes)awidthshow
162 79 gm
(were well known or in a small number.)show
173 79 gm
1.19873 0. 32 0.11987 0.(The core algorithm for dynamic splitting allows that any node can be a splitting node. Data on)awidthshow
184 79 gm
1.79733 0. 32 0.17973 0.(arbitrary nodes is much more expensive to transmit and to receive: communication overhead)awidthshow
195 79 gm
(increases, especially on a network of workstations.)show
206 79 gm
0.08758 0. 32 0.00875 0.(Moreover, each task has to be identified independently form the worker that executes it; thus to each)awidthshow
217 79 gm
1.59393 0. 32 0.15939 0.(node N we associate a signature that will be inherited by all N successors; such an idea was)awidthshow
228 79 gm
1.32034 0. 32 0.13203 0.(introduced in [Eli90]. When a cut occurs, all parallel search having the same signature will be)awidthshow
239 79 gm
(terminated, because they are now useless.)show
250 79 gm
0.01724 0. 32 0.00172 0.(Each new splitting node is associated to a new signature; since in the core algorithm a parallel search)awidthshow
261 79 gm
0.26687 0. 32 0.02668 0.(can be started at any level in the tree, nodes of the same subtree obtain different signatures. When a)awidthshow
272 79 gm
0.44692 0. 32 0.04469 0.(cut is generated for the top-level of a subtree all parallel searches of its branches should terminate,)awidthshow
283 79 gm
0.81695 0. 32 0.08169 0.(even if the signatures are different. The signature is a distributed data structure whose root is the)awidthshow
294 79 gm
0.65292 0. 32 0.06529 0.(signature of the game tree root. Suppose that a node N has a signature S inherited from its father;)awidthshow
305 79 gm
(suppose that N is chosen as splitting node: it get s a new signature T.)show
(nc 330 96 543 506 6 rc)kp
64 gr
412 146 435 169 1 ov
0 gr
412.5 146.5 434.5 168.5 0 ov
64 gr
468 113 490 135 1 ov
0 gr
468.5 113.5 489.5 134.5 0 ov
64 gr
519 98 542 120 1 ov
0 gr
519.5 98.5 541.5 119.5 0 ov
64 gr
519 126 542 148 1 ov
0 gr
519.5 126.5 541.5 147.5 0 ov
489 124 gm
519 136 lin
489 124 gm
519 108 lin
64 gr
468 175 490 198 1 ov
0 gr
468.5 175.5 489.5 197.5 0 ov
64 gr
519 160 542 182 1 ov
0 gr
519.5 160.5 541.5 181.5 0 ov
64 gr
519 188 542 210 1 ov
0 gr
519.5 188.5 541.5 209.5 0 ov
489 186 gm
519 199 lin
489 186 gm
519 170 lin
434 156 gm
468 187 lin
434 156 gm
468 123 lin
64 gr
412 278 435 300 1 ov
0 gr
412.5 278.5 434.5 299.5 0 ov
64 gr
468 245 490 267 1 ov
0 gr
468.5 245.5 489.5 266.5 0 ov
64 gr
519 229 542 252 1 ov
0 gr
519.5 229.5 541.5 251.5 0 ov
64 gr
519 258 542 280 1 ov
0 gr
519.5 258.5 541.5 279.5 0 ov
489 256 gm
519 268 lin
0 0 2 9 6 2 dh
489 256 gm
519 240 lin
rh
psb
pse
64 gr
468 307 490 330 1 ov
0 gr
468.5 307.5 489.5 329.5 0 ov
64 gr
519 292 542 314 1 ov
0 gr
519.5 292.5 541.5 313.5 0 ov
64 gr
519 320 542 342 1 ov
0 gr
519.5 320.5 541.5 341.5 0 ov
489 318 gm
519 331 lin
489 318 gm
519 302 lin
434 288 gm
468 319 lin
434 288 gm
468 256 lin
64 gr
413 410 436 432 1 ov
0 gr
413.5 410.5 435.5 431.5 0 ov
64 gr
468 377 490 399 1 ov
0 gr
468.5 377.5 489.5 398.5 0 ov
64 gr
519 361 542 383 1 ov
0 gr
519.5 361.5 541.5 382.5 0 ov
64 gr
519 389 542 412 1 ov
0 gr
519.5 389.5 541.5 411.5 0 ov
0 0 2 9 6 2 dh
489 387 gm
519 400 lin
rh
psb
pse
489 387 gm
519 372 lin
64 gr
469 439 491 461 1 ov
0 gr
469.5 439.5 490.5 460.5 0 ov
64 gr
520 423 543 446 1 ov
0 gr
520.5 423.5 542.5 445.5 0 ov
64 gr
519 452 542 474 1 ov
0 gr
519.5 452.5 541.5 473.5 0 ov
489 450 gm
519 462 lin
489 450 gm
519 434 lin
434 420 gm
468 450 lin
0 0 2 9 6 2 dh
434 420 gm
468 387 lin
rh
psb
pse
64 gr
353 278 375 300 1 ov
0 gr
353.5 278.5 374.5 299.5 0 ov
0 0 2 9 6 2 dh
374 290 gm
412 290 lin
rh
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0 0 2 9 6 2 dh
374 290 gm
412 158 lin
rh
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374 289 gm
412 420 lin
64 gr
361 282 368 300 1 rc
366 283 gm
(nc 361 282 368 300 6 rc)kp
F 1 setTxMode
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417 154 429 162 1 rc
426 155 gm
(nc 417 154 429 162 6 rc)kp
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417 285 429 293 1 rc
426 286 gm
(nc 417 285 429 293 6 rc)kp
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(1)show
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425 414 gm
(nc 420 413 427 430 6 rc)kp
F 1 setTxMode
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(nc 330 96 543 506 6 rc)kp
64 gr
475 250 482 267 1 rc
480 251 gm
(nc 475 250 482 267 6 rc)kp
F 1 setTxMode
(1)show
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480 262 gm
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(nc 330 96 543 506 6 rc)kp
64 gr
524 267 536 275 1 rc
533 268 gm
(nc 524 267 536 275 6 rc)kp
F 1 setTxMode
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(nc 330 96 543 506 6 rc)kp
64 gr
525 329 537 337 1 rc
534 330 gm
(nc 525 329 537 337 6 rc)kp
F 1 setTxMode
(1)show
(nc 330 96 543 506 6 rc)kp
64 gr
523 301 535 309 1 rc
532 302 gm
(nc 523 301 535 309 6 rc)kp
F 1 setTxMode
(1)show
(nc 330 96 543 506 6 rc)kp
64 gr
524 239 536 247 1 rc
533 240 gm
(nc 524 239 536 247 6 rc)kp
F 1 setTxMode
(3)show
(nc 330 96 543 506 6 rc)kp
64 gr
473 185 485 193 1 rc
482 186 gm
(nc 473 185 485 193 6 rc)kp
F 1 setTxMode
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(nc 330 96 543 506 6 rc)kp
64 gr
524 198 536 206 1 rc
533 199 gm
(nc 524 198 536 206 6 rc)kp
F 1 setTxMode
(1)show
(nc 330 96 543 506 6 rc)kp
64 gr
524 169 536 177 1 rc
533 170 gm
(nc 524 169 536 177 6 rc)kp
F 1 setTxMode
(1)show
(nc 330 96 543 506 6 rc)kp
64 gr
524 136 536 144 1 rc
533 137 gm
(nc 524 136 536 144 6 rc)kp
F 1 setTxMode
(1)show
(nc 330 96 543 506 6 rc)kp
64 gr
524 107 536 115 1 rc
533 108 gm
(nc 524 107 536 115 6 rc)kp
F 1 setTxMode
(1)show
(nc 330 96 543 506 6 rc)kp
64 gr
472 122 484 130 1 rc
481 123 gm
(nc 472 122 484 130 6 rc)kp
F 1 setTxMode
(1)show
(nc 330 96 543 506 6 rc)kp
64 gr
471 317 483 325 1 rc
480 318 gm
(nc 471 317 483 325 6 rc)kp
F 1 setTxMode
(1)show
(nc 330 96 543 506 6 rc)kp
64 gr
474 382 481 399 1 rc
479 383 gm
(nc 474 382 481 399 6 rc)kp
F 1 setTxMode
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479 394 gm
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(4)show
(nc 330 96 543 506 6 rc)kp
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472 448 484 456 1 rc
481 449 gm
(nc 472 448 484 456 6 rc)kp
F 1 setTxMode
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(2)show
(nc 330 96 543 506 6 rc)kp
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524 432 536 440 1 rc
533 433 gm
(nc 524 432 536 440 6 rc)kp
F 1 setTxMode
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(nc 330 96 543 506 6 rc)kp
64 gr
524 461 536 469 1 rc
533 462 gm
(nc 524 461 536 469 6 rc)kp
F 1 setTxMode
(2)show
(nc 330 96 543 506 6 rc)kp
64 gr
524 369 536 377 1 rc
533 370 gm
(nc 524 369 536 377 6 rc)kp
F 1 setTxMode
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(nc 330 96 543 506 6 rc)kp
64 gr
524 399 536 407 1 rc
533 400 gm
(nc 524 399 536 407 6 rc)kp
F 1 setTxMode
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(nc 330 96 543 506 6 rc)kp
64 gr
376 215 388 229 1 rc
385 216 gm
(nc 376 215 388 229 6 rc)kp
F 1 setTxMode
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(nc 330 96 543 506 6 rc)kp
64 gr
437 388 449 402 1 rc
446 389 gm
(nc 437 388 449 402 6 rc)kp
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(nc 330 96 543 506 6 rc)kp
64 gr
495 232 507 246 1 rc
504 233 gm
(nc 495 232 507 246 6 rc)kp
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(nc 330 96 543 506 6 rc)kp
64 gr
492 364 504 378 1 rc
501 365 gm
(nc 492 364 504 378 6 rc)kp
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0 0 pen
355 317 gm
(nc 330 96 543 506 6 rc)kp
64 gr
355 317 lin
nc ct 39 0 put
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360 308 pl
355 317 pl
358 318 pl
362 318 pl
360 308 pl
4 ep
360 308 gm
bp
355 317 T qi
355 317 qc
358 318 qc
358 318 qc
362 318 qc
362 318 qc
360 308 qc
360 308 T qq
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ef
0 gr
15 ec
(nc 330 96 543 506 6 rc)kp
1 1 pen
358 318 gm
0 gr
350 376 lin
64 gr
332 377 382 506 1 rc
0 gr
332.5 377.5 381.5 505.5 0 rc
64 gr
333 386 381 494 1 rc
342 387 gm
(nc 333 386 381 494 6 rc)kp
F 1 setTxMode
(A decomposition node)show
354 387 gm
(defines a signature)show
366 387 gm
(different from that)show
378 387 gm
(inherited from the father)show
318 77 gm
(nc 30 28 811 566 6 rc)kp
0 gr
318 525 lin
572 235 gm
F 1 setTxMode
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(Fig.18)show
1 fs
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( Assigning a signature)show
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0.43762 0. 32 0.04376 0.(In Fig.18 it is shown a game tree; dotted lines represents subtrees distributed to other processors; a)awidthshow
620 79 gm
0.45349 0. 32 0.04534 0.(node label is the local signature. The depicted game tree includes four local splittings. Splitting \(a\))awidthshow
631 79 gm
(distributes tasks for searching leftmost subtrees; other splittings distribute a single task only.)show
661 79 gm
1 fs
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(5.4 Results)show
674 79 gm
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0.35888 0. 32 0.03588 0.(We tested the algorithm for dynamic splitting with several splitting criteria; we found that the most)awidthshow
685 79 gm
(interesting were the following:)show
697 88 gm
0.18385 0.(\245\312)ashow
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1.16302 0. 32 0.11630 0.(Policy A)awidthshow
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1.10183 0. 32 0.11018 0.(: local condition: young)awidthshow
697 244 gm
0.95367 0. 32 0.09536 0.(-brothers-wait without distributing small subtrees \(depth)awidthshow
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0.95367 0. 32 0.09536 0.(2\);)awidthshow
708 101 gm
0.14068 0. 32 0.01406 0.(global condition: splitting is allowed only if there is an idle worker and the agenda contains \(P)awidthshow
708 519 gm
(-)show
719 101 gm
(1\) tasks.)show
732 88 gm
(\245\312)show
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(Policy B)show
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(: no signature tree; splitting is allowed even if there are no idle workers.)show
744 79 gm
(The corresponding tests are shown in Figg.19 and 20.)show
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(A Comparison of Parallel Search Algorithms)show
773 79 gm
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(T\312\(sec\))show
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122 294 gm
122 327 lin
124 294 gm
124 327 lin
122 328 gm
122 330 lin
124 328 gm
124 330 lin
122 331 gm
122 364 lin
124 331 gm
124 364 lin
122 365 gm
122 367 lin
124 365 gm
124 367 lin
122 368 gm
122 400 lin
124 368 gm
124 400 lin
122 401 gm
122 403 lin
124 401 gm
124 403 lin
122 404 gm
122 487 lin
124 404 gm
124 487 lin
122 488 gm
122 490 lin
124 488 gm
124 490 lin
122 491 gm
122 524 lin
124 491 gm
124 524 lin
122 525 gm
122 527 lin
124 527 lin
124 525 gm
124 525 lin
124 525 lin
125 80 gm
138 80 lin
125 82 gm
138 82 lin
125 132 gm
138 132 lin
125 134 gm
138 134 lin
125 183 gm
138 183 lin
125 185 gm
138 185 lin
125 254 gm
138 254 lin
125 256 gm
138 256 lin
125 291 gm
138 291 lin
125 293 gm
138 293 lin
125 328 gm
138 328 lin
125 330 gm
138 330 lin
125 365 gm
138 365 lin
125 367 gm
138 367 lin
125 401 gm
138 401 lin
125 403 gm
138 403 lin
125 488 gm
138 488 lin
125 490 gm
138 490 lin
125 525 gm
138 525 lin
125 527 gm
138 527 lin
153 105 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
152 149 gm
(8301)show
152 203 gm
(5347545)show
152 269 gm
(---)show
152 306 gm
(---)show
152 343 gm
(---)show
152 380 gm
(---)show
152 439 gm
(644)show
152 503 gm
(---)show
139 82 gm
0 gr
141 82 lin
139 80 gm
141 80 lin
139 83 gm
139 131 lin
141 83 gm
141 131 lin
139 134 gm
139 134 lin
141 132 gm
141 132 lin
139 132 gm
139 132 lin
141 134 gm
141 134 lin
139 135 gm
139 182 lin
141 135 gm
141 182 lin
139 185 gm
139 185 lin
141 183 gm
141 183 lin
139 183 gm
139 183 lin
141 185 gm
141 185 lin
139 186 gm
139 253 lin
141 186 gm
141 253 lin
139 256 gm
139 256 lin
141 254 gm
141 254 lin
139 254 gm
139 254 lin
141 256 gm
141 256 lin
139 257 gm
139 290 lin
141 257 gm
141 290 lin
139 293 gm
139 293 lin
141 291 gm
141 291 lin
139 291 gm
139 291 lin
141 293 gm
141 293 lin
139 294 gm
139 327 lin
141 294 gm
141 327 lin
139 330 gm
139 330 lin
141 328 gm
141 328 lin
139 328 gm
139 328 lin
141 330 gm
141 330 lin
139 331 gm
139 364 lin
141 331 gm
141 364 lin
139 367 gm
139 367 lin
141 365 gm
141 365 lin
139 365 gm
139 365 lin
141 367 gm
141 367 lin
139 368 gm
139 400 lin
141 368 gm
141 400 lin
139 403 gm
139 403 lin
141 401 gm
141 401 lin
139 401 gm
139 401 lin
141 403 gm
141 403 lin
139 404 gm
139 487 lin
141 404 gm
141 487 lin
139 490 gm
139 490 lin
141 488 gm
141 488 lin
139 488 gm
139 488 lin
141 490 gm
141 490 lin
139 491 gm
139 524 lin
141 491 gm
141 524 lin
139 527 gm
141 527 lin
139 525 gm
141 525 lin
142 80 gm
155 80 lin
142 82 gm
155 82 lin
142 132 gm
155 132 lin
142 134 gm
155 134 lin
142 183 gm
155 183 lin
142 185 gm
155 185 lin
142 254 gm
155 254 lin
142 256 gm
155 256 lin
142 291 gm
155 291 lin
142 293 gm
155 293 lin
142 328 gm
155 328 lin
142 330 gm
155 330 lin
142 365 gm
155 365 lin
142 367 gm
155 367 lin
142 401 gm
155 401 lin
142 403 gm
155 403 lin
142 488 gm
155 488 lin
142 490 gm
155 490 lin
142 525 gm
155 525 lin
142 527 gm
155 527 lin
167 105 gm
F 1 setTxMode
(3)show
167 149 gm
(3797)show
167 203 gm
(6206534)show
167 265 gm
(2.19)show
167 302 gm
(0.73)show
167 339 gm
(0.85)show
167 376 gm
(0.16)show
167 436 gm
(1635)show
167 499 gm
(2.54)show
156 82 gm
0 gr
156 82 lin
156 80 gm
156 80 lin
156 83 gm
156 131 lin
156 134 gm
156 134 lin
156 132 gm
156 132 lin
156 135 gm
156 182 lin
156 185 gm
156 185 lin
156 183 gm
156 183 lin
156 186 gm
156 253 lin
156 256 gm
156 256 lin
156 254 gm
156 254 lin
156 257 gm
156 290 lin
156 293 gm
156 293 lin
156 291 gm
156 291 lin
156 294 gm
156 327 lin
156 330 gm
156 330 lin
156 328 gm
156 328 lin
156 331 gm
156 364 lin
156 367 gm
156 367 lin
156 365 gm
156 365 lin
156 368 gm
156 400 lin
156 403 gm
156 403 lin
156 401 gm
156 401 lin
156 404 gm
156 487 lin
156 490 gm
156 490 lin
156 488 gm
156 488 lin
156 491 gm
156 524 lin
156 527 gm
156 527 lin
156 525 gm
156 525 lin
157 80 gm
169 80 lin
157 82 gm
169 82 lin
157 132 gm
169 132 lin
157 134 gm
169 134 lin
157 183 gm
169 183 lin
157 185 gm
169 185 lin
157 254 gm
169 254 lin
157 256 gm
169 256 lin
157 291 gm
169 291 lin
157 293 gm
169 293 lin
157 328 gm
169 328 lin
157 330 gm
169 330 lin
157 365 gm
169 365 lin
157 367 gm
169 367 lin
157 401 gm
169 401 lin
157 403 gm
169 403 lin
157 488 gm
169 488 lin
157 490 gm
169 490 lin
157 525 gm
169 525 lin
157 527 gm
169 527 lin
181 105 gm
F 1 setTxMode
(5)show
181 149 gm
(2634)show
181 203 gm
(6829036)show
181 265 gm
(3.15)show
181 302 gm
(0.63)show
181 339 gm
(0.82)show
181 376 gm
(0.28)show
181 436 gm
(2593)show
181 499 gm
(4.02)show
170 82 gm
0 gr
170 82 lin
170 80 gm
170 80 lin
170 83 gm
170 131 lin
170 134 gm
170 134 lin
170 132 gm
170 132 lin
170 135 gm
170 182 lin
170 185 gm
170 185 lin
170 183 gm
170 183 lin
170 186 gm
170 253 lin
170 256 gm
170 256 lin
170 254 gm
170 254 lin
170 257 gm
170 290 lin
170 293 gm
170 293 lin
170 291 gm
170 291 lin
170 294 gm
170 327 lin
170 330 gm
170 330 lin
170 328 gm
170 328 lin
170 331 gm
170 364 lin
170 367 gm
170 367 lin
170 365 gm
170 365 lin
170 368 gm
170 400 lin
170 403 gm
170 403 lin
170 401 gm
170 401 lin
170 404 gm
170 487 lin
170 490 gm
170 490 lin
170 488 gm
170 488 lin
170 491 gm
170 524 lin
170 527 gm
170 527 lin
170 525 gm
170 525 lin
171 80 gm
183 80 lin
171 82 gm
183 82 lin
171 132 gm
183 132 lin
171 134 gm
183 134 lin
171 183 gm
183 183 lin
171 185 gm
183 185 lin
171 254 gm
183 254 lin
171 256 gm
183 256 lin
171 291 gm
183 291 lin
171 293 gm
183 293 lin
171 328 gm
183 328 lin
171 330 gm
183 330 lin
171 365 gm
183 365 lin
171 367 gm
183 367 lin
171 401 gm
183 401 lin
171 403 gm
183 403 lin
171 488 gm
183 488 lin
171 490 gm
183 490 lin
171 525 gm
183 525 lin
171 527 gm
183 527 lin
196 105 gm
F 1 setTxMode
(7)show
196 149 gm
(2133)show
196 203 gm
(7407997)show
196 265 gm
(3.89)show
196 302 gm
(0.56)show
196 339 gm
(0.77)show
196 376 gm
(0.39)show
196 436 gm
(3473)show
196 499 gm
(5.39)show
184 82 gm
0 gr
184 82 lin
184 80 gm
184 80 lin
184 83 gm
184 131 lin
184 134 gm
184 134 lin
184 132 gm
184 132 lin
184 135 gm
184 182 lin
184 185 gm
184 185 lin
184 183 gm
184 183 lin
184 186 gm
184 253 lin
184 256 gm
184 256 lin
184 254 gm
184 254 lin
184 257 gm
184 290 lin
184 293 gm
184 293 lin
184 291 gm
184 291 lin
184 294 gm
184 327 lin
184 330 gm
184 330 lin
184 328 gm
184 328 lin
184 331 gm
184 364 lin
184 367 gm
184 367 lin
184 365 gm
184 365 lin
184 368 gm
184 400 lin
184 403 gm
184 403 lin
184 401 gm
184 401 lin
184 404 gm
184 487 lin
184 490 gm
184 490 lin
184 488 gm
184 488 lin
184 491 gm
184 524 lin
184 527 gm
184 527 lin
184 525 gm
184 525 lin
185 80 gm
198 80 lin
185 82 gm
198 82 lin
185 132 gm
198 132 lin
185 134 gm
198 134 lin
185 183 gm
198 183 lin
185 185 gm
198 185 lin
185 254 gm
198 254 lin
185 256 gm
198 256 lin
185 291 gm
198 291 lin
185 293 gm
198 293 lin
185 328 gm
198 328 lin
185 330 gm
198 330 lin
185 365 gm
198 365 lin
185 367 gm
198 367 lin
185 401 gm
198 401 lin
185 403 gm
198 403 lin
185 488 gm
198 488 lin
185 490 gm
198 490 lin
185 525 gm
198 525 lin
185 527 gm
198 527 lin
211 105 gm
F 1 setTxMode
(9)show
211 149 gm
(1878)show
211 203 gm
(7810188)show
211 265 gm
(4.42)show
211 302 gm
(0.49)show
211 339 gm
(0.74)show
211 376 gm
(0.46)show
211 436 gm
(4159)show
211 499 gm
(6.46)show
199 82 gm
0 gr
199 82 lin
199 80 gm
199 80 lin
199 83 gm
199 131 lin
199 134 gm
199 134 lin
199 132 gm
199 132 lin
199 135 gm
199 182 lin
199 185 gm
199 185 lin
199 183 gm
199 183 lin
199 186 gm
199 253 lin
199 256 gm
199 256 lin
199 254 gm
199 254 lin
199 257 gm
199 290 lin
199 293 gm
199 293 lin
199 291 gm
199 291 lin
199 294 gm
199 327 lin
199 330 gm
199 330 lin
199 328 gm
199 328 lin
199 331 gm
199 364 lin
199 367 gm
199 367 lin
199 365 gm
199 365 lin
199 368 gm
199 400 lin
199 403 gm
199 403 lin
199 401 gm
199 401 lin
199 404 gm
199 487 lin
199 490 gm
199 490 lin
199 488 gm
199 488 lin
199 491 gm
199 524 lin
199 527 gm
199 527 lin
199 525 gm
199 525 lin
200 80 gm
213 80 lin
200 82 gm
213 82 lin
200 132 gm
213 132 lin
200 134 gm
213 134 lin
200 183 gm
213 183 lin
200 185 gm
213 185 lin
200 254 gm
213 254 lin
200 256 gm
213 256 lin
200 291 gm
213 291 lin
200 293 gm
213 293 lin
200 328 gm
213 328 lin
200 330 gm
213 330 lin
200 365 gm
213 365 lin
200 367 gm
213 367 lin
200 401 gm
213 401 lin
200 403 gm
213 403 lin
200 488 gm
213 488 lin
200 490 gm
213 490 lin
200 525 gm
213 525 lin
200 527 gm
213 527 lin
225 103 gm
F 1 setTxMode
(11)show
225 149 gm
(1699)show
225 203 gm
(8205839)show
225 265 gm
(4.89)show
225 302 gm
(0.44)show
225 339 gm
(0.70)show
225 376 gm
(0.53)show
225 436 gm
(4830)show
225 499 gm
(7.50)show
214 82 gm
0 gr
214 82 lin
214 80 gm
214 80 lin
214 83 gm
214 131 lin
214 134 gm
214 134 lin
214 132 gm
214 132 lin
214 135 gm
214 182 lin
214 185 gm
214 185 lin
214 183 gm
214 183 lin
214 186 gm
214 253 lin
214 256 gm
214 256 lin
214 254 gm
214 254 lin
214 257 gm
214 290 lin
214 293 gm
214 293 lin
214 291 gm
214 291 lin
214 294 gm
214 327 lin
214 330 gm
214 330 lin
214 328 gm
214 328 lin
214 331 gm
214 364 lin
214 367 gm
214 367 lin
214 365 gm
214 365 lin
214 368 gm
214 400 lin
214 403 gm
214 403 lin
214 401 gm
214 401 lin
214 404 gm
214 487 lin
214 490 gm
214 490 lin
214 488 gm
214 488 lin
214 491 gm
214 524 lin
214 527 gm
214 527 lin
214 525 gm
214 525 lin
215 80 gm
227 80 lin
215 82 gm
227 82 lin
230 80 gm
230 82 lin
228 80 gm
230 80 lin
228 82 gm
228 82 lin
228 82 lin
228 83 gm
228 131 lin
230 83 gm
230 131 lin
215 132 gm
227 132 lin
215 134 gm
227 134 lin
228 132 gm
228 134 lin
230 132 gm
230 134 lin
228 135 gm
228 182 lin
230 135 gm
230 182 lin
215 183 gm
227 183 lin
215 185 gm
227 185 lin
228 183 gm
228 185 lin
230 183 gm
230 185 lin
228 186 gm
228 253 lin
230 186 gm
230 253 lin
215 254 gm
227 254 lin
215 256 gm
227 256 lin
228 254 gm
228 256 lin
230 254 gm
230 256 lin
228 257 gm
228 290 lin
230 257 gm
230 290 lin
215 291 gm
227 291 lin
215 293 gm
227 293 lin
228 291 gm
228 293 lin
230 291 gm
230 293 lin
228 294 gm
228 327 lin
230 294 gm
230 327 lin
215 328 gm
227 328 lin
215 330 gm
227 330 lin
228 328 gm
228 330 lin
230 328 gm
230 330 lin
228 331 gm
228 364 lin
230 331 gm
230 364 lin
215 365 gm
227 365 lin
215 367 gm
227 367 lin
228 365 gm
228 367 lin
230 365 gm
230 367 lin
228 368 gm
228 400 lin
230 368 gm
230 400 lin
215 401 gm
227 401 lin
215 403 gm
227 403 lin
228 401 gm
228 403 lin
230 401 gm
230 403 lin
228 404 gm
228 487 lin
230 404 gm
230 487 lin
215 488 gm
227 488 lin
215 490 gm
227 490 lin
228 488 gm
228 490 lin
230 488 gm
230 490 lin
228 491 gm
228 524 lin
230 491 gm
230 524 lin
215 525 gm
227 525 lin
215 527 gm
227 527 lin
230 525 gm
230 527 lin
228 527 gm
230 527 lin
228 525 gm
228 525 lin
228 525 lin
242 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig.19)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(Young-brothers-wait \(Policy A\))show
276 96 gm
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Procs)show
276 145 gm
(T\312\(sec\))show
276 200 gm
(N\312\(nodes\))show
276 271 gm
(S)show
276 308 gm
(E)show
276 338 gm
(Fpm)show
276 378 gm
(SO)show
276 416 gm
(SS\312\(nodes/sec\))show
276 502 gm
(Sss)show
262 80 gm
0 gr
262 82 lin
262 80 gm
264 80 lin
264 82 gm
264 82 lin
264 82 lin
262 83 gm
262 131 lin
264 83 gm
264 131 lin
262 132 gm
262 134 lin
264 132 gm
264 134 lin
262 135 gm
262 182 lin
264 135 gm
264 182 lin
262 183 gm
262 185 lin
264 183 gm
264 185 lin
262 186 gm
262 253 lin
264 186 gm
264 253 lin
262 254 gm
262 256 lin
264 254 gm
264 256 lin
262 257 gm
262 290 lin
264 257 gm
264 290 lin
262 291 gm
262 293 lin
264 291 gm
264 293 lin
262 294 gm
262 327 lin
264 294 gm
264 327 lin
262 328 gm
262 330 lin
264 328 gm
264 330 lin
262 331 gm
262 364 lin
264 331 gm
264 364 lin
262 365 gm
262 367 lin
264 365 gm
264 367 lin
262 368 gm
262 400 lin
264 368 gm
264 400 lin
262 401 gm
262 403 lin
264 401 gm
264 403 lin
262 404 gm
262 487 lin
264 404 gm
264 487 lin
262 488 gm
262 490 lin
264 488 gm
264 490 lin
262 491 gm
262 524 lin
264 491 gm
264 524 lin
262 525 gm
262 527 lin
264 527 lin
264 525 gm
264 525 lin
264 525 lin
265 80 gm
278 80 lin
265 82 gm
278 82 lin
265 132 gm
278 132 lin
265 134 gm
278 134 lin
265 183 gm
278 183 lin
265 185 gm
278 185 lin
265 254 gm
278 254 lin
265 256 gm
278 256 lin
265 291 gm
278 291 lin
265 293 gm
278 293 lin
265 328 gm
278 328 lin
265 330 gm
278 330 lin
265 365 gm
278 365 lin
265 367 gm
278 367 lin
265 401 gm
278 401 lin
265 403 gm
278 403 lin
265 488 gm
278 488 lin
265 490 gm
278 490 lin
265 525 gm
278 525 lin
265 527 gm
278 527 lin
293 105 gm
F 1 setTxMode
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(1)show
293 149 gm
(8301)show
293 203 gm
(5347545)show
293 269 gm
(---)show
293 306 gm
(---)show
293 343 gm
(---)show
293 380 gm
(---)show
293 439 gm
(644)show
293 503 gm
(---)show
279 82 gm
0 gr
281 82 lin
279 80 gm
281 80 lin
279 83 gm
279 131 lin
281 83 gm
281 131 lin
279 134 gm
279 134 lin
281 132 gm
281 132 lin
279 132 gm
279 132 lin
281 134 gm
281 134 lin
279 135 gm
279 182 lin
281 135 gm
281 182 lin
279 185 gm
279 185 lin
281 183 gm
281 183 lin
279 183 gm
279 183 lin
281 185 gm
281 185 lin
279 186 gm
279 253 lin
281 186 gm
281 253 lin
279 256 gm
279 256 lin
281 254 gm
281 254 lin
279 254 gm
279 254 lin
281 256 gm
281 256 lin
279 257 gm
279 290 lin
281 257 gm
281 290 lin
279 293 gm
279 293 lin
281 291 gm
281 291 lin
279 291 gm
279 291 lin
281 293 gm
281 293 lin
279 294 gm
279 327 lin
281 294 gm
281 327 lin
279 330 gm
279 330 lin
281 328 gm
281 328 lin
279 328 gm
279 328 lin
281 330 gm
281 330 lin
279 331 gm
279 364 lin
281 331 gm
281 364 lin
279 367 gm
279 367 lin
281 365 gm
281 365 lin
279 365 gm
279 365 lin
281 367 gm
281 367 lin
279 368 gm
279 400 lin
281 368 gm
281 400 lin
279 403 gm
279 403 lin
281 401 gm
281 401 lin
279 401 gm
279 401 lin
281 403 gm
281 403 lin
279 404 gm
279 487 lin
281 404 gm
281 487 lin
279 490 gm
279 490 lin
281 488 gm
281 488 lin
279 488 gm
279 488 lin
281 490 gm
281 490 lin
279 491 gm
279 524 lin
281 491 gm
281 524 lin
279 527 gm
281 527 lin
279 525 gm
281 525 lin
282 80 gm
295 80 lin
282 82 gm
295 82 lin
282 132 gm
295 132 lin
282 134 gm
295 134 lin
282 183 gm
295 183 lin
282 185 gm
295 185 lin
282 254 gm
295 254 lin
282 256 gm
295 256 lin
282 291 gm
295 291 lin
282 293 gm
295 293 lin
282 328 gm
295 328 lin
282 330 gm
295 330 lin
282 365 gm
295 365 lin
282 367 gm
295 367 lin
282 401 gm
295 401 lin
282 403 gm
295 403 lin
282 488 gm
295 488 lin
282 490 gm
295 490 lin
282 525 gm
295 525 lin
282 527 gm
295 527 lin
308 105 gm
F 1 setTxMode
(3)show
308 149 gm
(4629)show
308 203 gm
(6476838)show
308 265 gm
(1.79)show
308 302 gm
(0.60)show
308 339 gm
(0.84)show
308 376 gm
(0.21)show
308 436 gm
(1399)show
308 499 gm
(2.17)show
296 82 gm
0 gr
296 82 lin
296 80 gm
296 80 lin
296 83 gm
296 131 lin
296 134 gm
296 134 lin
296 132 gm
296 132 lin
296 135 gm
296 182 lin
296 185 gm
296 185 lin
296 183 gm
296 183 lin
296 186 gm
296 253 lin
296 256 gm
296 256 lin
296 254 gm
296 254 lin
296 257 gm
296 290 lin
296 293 gm
296 293 lin
296 291 gm
296 291 lin
296 294 gm
296 327 lin
296 330 gm
296 330 lin
296 328 gm
296 328 lin
296 331 gm
296 364 lin
296 367 gm
296 367 lin
296 365 gm
296 365 lin
296 368 gm
296 400 lin
296 403 gm
296 403 lin
296 401 gm
296 401 lin
296 404 gm
296 487 lin
296 490 gm
296 490 lin
296 488 gm
296 488 lin
296 491 gm
296 524 lin
296 527 gm
296 527 lin
296 525 gm
296 525 lin
297 80 gm
310 80 lin
297 82 gm
310 82 lin
297 132 gm
310 132 lin
297 134 gm
310 134 lin
297 183 gm
310 183 lin
297 185 gm
310 185 lin
297 254 gm
310 254 lin
297 256 gm
310 256 lin
297 291 gm
310 291 lin
297 293 gm
310 293 lin
297 328 gm
310 328 lin
297 330 gm
310 330 lin
297 365 gm
310 365 lin
297 367 gm
310 367 lin
297 401 gm
310 401 lin
297 403 gm
310 403 lin
297 488 gm
310 488 lin
297 490 gm
310 490 lin
297 525 gm
310 525 lin
297 527 gm
310 527 lin
323 105 gm
F 1 setTxMode
(5)show
323 149 gm
(2798)show
323 203 gm
(7280335)show
323 265 gm
(2.97)show
323 302 gm
(0.59)show
323 339 gm
(0.88)show
323 376 gm
(0.36)show
323 436 gm
(2602)show
323 499 gm
(4.04)show
311 82 gm
0 gr
311 82 lin
311 80 gm
311 80 lin
311 83 gm
311 131 lin
311 134 gm
311 134 lin
311 132 gm
311 132 lin
311 135 gm
311 182 lin
311 185 gm
311 185 lin
311 183 gm
311 183 lin
311 186 gm
311 253 lin
311 256 gm
311 256 lin
311 254 gm
311 254 lin
311 257 gm
311 290 lin
311 293 gm
311 293 lin
311 291 gm
311 291 lin
311 294 gm
311 327 lin
311 330 gm
311 330 lin
311 328 gm
311 328 lin
311 331 gm
311 364 lin
311 367 gm
311 367 lin
311 365 gm
311 365 lin
311 368 gm
311 400 lin
311 403 gm
311 403 lin
311 401 gm
311 401 lin
311 404 gm
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325 525 lin
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325 527 lin
338 105 gm
F 1 setTxMode
(7)show
338 149 gm
(2223)show
338 203 gm
(8133582)show
338 265 gm
(3.73)show
338 302 gm
(0.53)show
338 339 gm
(0.89)show
338 376 gm
(0.52)show
338 436 gm
(3659)show
338 499 gm
(5.68)show
326 82 gm
0 gr
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340 403 lin
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327 525 gm
340 525 lin
327 527 gm
340 527 lin
353 105 gm
F 1 setTxMode
(9)show
353 149 gm
(1972)show
353 203 gm
(8541944)show
353 265 gm
(4.21)show
353 302 gm
(0.47)show
353 339 gm
(0.89)show
353 376 gm
(0.60)show
353 436 gm
(4332)show
353 499 gm
(6.72)show
341 82 gm
0 gr
341 82 lin
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355 291 lin
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355 293 lin
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355 328 lin
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355 330 lin
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355 365 lin
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355 367 lin
342 401 gm
355 401 lin
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355 403 lin
342 488 gm
355 488 lin
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355 525 lin
342 527 gm
355 527 lin
368 103 gm
F 1 setTxMode
(11)show
368 149 gm
(1663)show
368 203 gm
(8689459)show
368 265 gm
(4.99)show
368 302 gm
(0.45)show
368 339 gm
(0.89)show
368 376 gm
(0.62)show
368 436 gm
(5225)show
368 499 gm
(8.11)show
356 82 gm
0 gr
356 82 lin
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370 367 lin
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373 365 gm
373 367 lin
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373 404 gm
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373 491 gm
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385 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
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(Fig.20)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
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(Young-brothers-wait \(Policy B\))show
401 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.80612 0. 32 0.08061 0.(These tables show several differences, although the policies are similar. Policy A gives a smaller)awidthshow
412 79 gm
0.13977 0. 32 0.01397 0.(search overhead, thanks to the signature tree; moreover, using less processors policy A is better than)awidthshow
423 79 gm
1.55426 0. 32 0.15542 0.(B. However, the production factor in A deteriorates with more processors, because the global)awidthshow
434 79 gm
0.20507 0. 32 0.02050 0.(condition it uses reduces the response time for each new task, even if there are "often" idle workers.)awidthshow
445 79 gm
0.20172 0. 32 0.02017 0.(On the other hand, policy B increments the average number of tasks in the agenda, and it lowers the)awidthshow
456 79 gm
0.15075 0. 32 0.01507 0.(coupling between the master and the workers. With 11 processors, we have a high production factor)awidthshow
467 79 gm
0.84869 0. 32 0.08486 0.(\(89%\). This algorithm results in a finer splitting and higher communication overhead due to task)awidthshow
478 79 gm
-0.00103 0.(distribution and collection of results. Let us try to analyze such an overhead. Look at the F)ashow
9 fz
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2 F /|______Times-Roman fnt
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(pm)show
11 fz
bu fc
2 F /|______Times-Roman fnt
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( column)show
489 79 gm
0.65643 0. 32 0.06564 0.(in Fig.21: such values include also communication overhead. Thus, we should split F)awidthshow
9 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.20443 0.(pm)ashow
11 fz
bu fc
2 F /|______Times-Roman fnt
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0.37826 0. 32 0.03782 0.( into F)awidthshow
9 fz
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0.25767 0.(pmr)ashow
500 79 gm
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
(\(real productivity\) e OC \(communication overhead\):)show
529 98 gm
1 fs
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(Procs)show
529 146 gm
(Fpm)show
529 181 gm
(Fpmr)show
529 223 gm
(OC)show
515 80 gm
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531 138 lin
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531 173 lin
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531 175 lin
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531 210 lin
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531 249 lin
546 107 gm
F 1 setTxMode
0 fs
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(3)show
546 147 gm
(0.85)show
546 184 gm
(0.84)show
546 221 gm
(0.01)show
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0 gr
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534 83 gm
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534 247 lin
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548 138 lin
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548 173 lin
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548 175 lin
535 210 gm
548 210 lin
535 212 gm
548 212 lin
535 247 gm
548 247 lin
535 249 gm
548 249 lin
561 107 gm
F 1 setTxMode
(5)show
561 147 gm
(0.88)show
561 184 gm
(0.80)show
561 221 gm
(0.08)show
549 82 gm
0 gr
549 82 lin
549 80 gm
549 80 lin
549 83 gm
549 135 lin
549 138 gm
549 138 lin
549 136 gm
549 136 lin
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549 172 lin
549 175 gm
549 175 lin
549 173 gm
549 173 lin
549 176 gm
549 209 lin
549 212 gm
549 212 lin
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549 210 lin
549 213 gm
549 246 lin
549 249 gm
549 249 lin
549 247 gm
549 247 lin
550 80 gm
563 80 lin
550 82 gm
563 82 lin
550 136 gm
563 136 lin
550 138 gm
563 138 lin
550 173 gm
563 173 lin
550 175 gm
563 175 lin
550 210 gm
563 210 lin
550 212 gm
563 212 lin
550 247 gm
563 247 lin
550 249 gm
563 249 lin
576 107 gm
F 1 setTxMode
(7)show
576 147 gm
(0.89)show
576 184 gm
(0.80)show
576 221 gm
(0.09)show
564 82 gm
0 gr
564 82 lin
564 80 gm
564 80 lin
564 83 gm
564 135 lin
564 138 gm
564 138 lin
564 136 gm
564 136 lin
564 139 gm
564 172 lin
564 175 gm
564 175 lin
564 173 gm
564 173 lin
564 176 gm
564 209 lin
564 212 gm
564 212 lin
564 210 gm
564 210 lin
564 213 gm
564 246 lin
564 249 gm
564 249 lin
564 247 gm
564 247 lin
565 80 gm
578 80 lin
565 82 gm
578 82 lin
565 136 gm
578 136 lin
565 138 gm
578 138 lin
565 173 gm
578 173 lin
565 175 gm
578 175 lin
565 210 gm
578 210 lin
565 212 gm
578 212 lin
565 247 gm
578 247 lin
565 249 gm
578 249 lin
591 107 gm
F 1 setTxMode
(9)show
591 147 gm
(0.89)show
591 184 gm
(0.75)show
591 221 gm
(0.14)show
579 82 gm
0 gr
579 82 lin
579 80 gm
579 80 lin
579 83 gm
579 135 lin
579 138 gm
579 138 lin
579 136 gm
579 136 lin
579 139 gm
579 172 lin
579 175 gm
579 175 lin
579 173 gm
579 173 lin
579 176 gm
579 209 lin
579 212 gm
579 212 lin
579 210 gm
579 210 lin
579 213 gm
579 246 lin
579 249 gm
579 249 lin
579 247 gm
579 247 lin
580 80 gm
593 80 lin
580 82 gm
593 82 lin
580 136 gm
593 136 lin
580 138 gm
593 138 lin
580 173 gm
593 173 lin
580 175 gm
593 175 lin
580 210 gm
593 210 lin
580 212 gm
593 212 lin
580 247 gm
593 247 lin
580 249 gm
593 249 lin
606 105 gm
F 1 setTxMode
(11)show
606 147 gm
(0.89)show
606 184 gm
(0.73)show
606 221 gm
(0.16)show
594 82 gm
0 gr
594 82 lin
594 80 gm
594 80 lin
594 83 gm
594 135 lin
594 138 gm
594 138 lin
594 136 gm
594 136 lin
594 139 gm
594 172 lin
594 175 gm
594 175 lin
594 173 gm
594 173 lin
594 176 gm
594 209 lin
594 212 gm
594 212 lin
594 210 gm
594 210 lin
594 213 gm
594 246 lin
594 249 gm
594 249 lin
594 247 gm
594 247 lin
595 80 gm
608 80 lin
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608 82 lin
611 80 gm
611 82 lin
609 80 gm
611 80 lin
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611 83 gm
611 135 lin
595 136 gm
608 136 lin
595 138 gm
608 138 lin
609 136 gm
609 138 lin
611 136 gm
611 138 lin
609 139 gm
609 172 lin
611 139 gm
611 172 lin
595 173 gm
608 173 lin
595 175 gm
608 175 lin
609 173 gm
609 175 lin
611 173 gm
611 175 lin
609 176 gm
609 209 lin
611 176 gm
611 209 lin
595 210 gm
608 210 lin
595 212 gm
608 212 lin
609 210 gm
609 212 lin
611 210 gm
611 212 lin
609 213 gm
609 246 lin
611 213 gm
611 246 lin
595 247 gm
608 247 lin
595 249 gm
608 249 lin
611 247 gm
611 249 lin
609 249 gm
611 249 lin
609 247 gm
609 247 lin
609 247 lin
623 79 gm
F 1 setTxMode
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
(Fig.21)show
0 fs
bu fc
2 F /|______Times-Roman fnt
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( )show
2 fs
bu fc
2 F /|______Times-Italic fnt
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(Policy B: analyizing the average production factor)show
639 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
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2.32254 0. 32 0.23225 0.(Such a table shows that the cost to be paid for communication overhead on a network of)awidthshow
650 79 gm
(workstations is high.)show
680 79 gm
1 fs
12 fz
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2 F /|______Times-Bold fnt
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(6. Conclusions)show
693 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.09750 0. 32 0.00975 0.(We have compared a number of parallel search algorithms in the domain of chess. We used Linda to)awidthshow
704 79 gm
2.65197 0. 32 0.26519 0.(develop two basic programs, one for static splitting and one for dynamic splitting. Their)awidthshow
715 79 gm
1.17568 0. 32 0.11756 0.(performances were progressively improved, especially using democratic cooperation with a low)awidthshow
726 79 gm
0.44967 0. 32 0.04496 0.(number of processors. For all algorithms we have sistematically measured the speedup S. We have)awidthshow
737 79 gm
0.63659 0. 32 0.06365 0.(seen that the theoretically optimum speedup S=N with N processors is impossible to reach for the)awidthshow
748 79 gm
(following reasons:)show
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(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
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(A Comparison of Parallel Search Algorithms)show
773 79 gm
(UBLCS-94-14)show
773 514 gm
(17)show
118 88 gm
11 fz
bu fc
2 F /|______Times-Roman fnt
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(\245\312commmunication overhead, given by messages betwen processors;)show
131 88 gm
(\245\312search overhead, given by duplication of subtree evaluation;)show
144 88 gm
(\245\312synchronisation overhead, given by bad load balancing.)show
156 79 gm
0.64361 0. 32 0.06436 0.(The most annoying problem is the coupling among these overheads: if we tried to reduce one, we)awidthshow
167 79 gm
0.73684 0. 32 0.07368 0.(got always an increase in another. For instance, the algorithm with dynamic splitting of the game)awidthshow
178 79 gm
0.86013 0. 32 0.08601 0.(tree top level \(Fig.15\) gives the best load balancing \(Fpm=90% with 11 processors\), but also the)awidthshow
189 79 gm
(worst search overhead \(SO=108% with 11 processors\).)show
200 79 gm
0.15335 0. 32 0.01533 0.(Thus, we searched for a tradeoff among the overheads. Our results say that the best results are given)awidthshow
211 79 gm
1.15768 0. 32 0.11576 0.(by PVSplit combined either with score sharing \(S=5.57 with 11 processors; see Fig.13\) or with)awidthshow
222 79 gm
(dynamic distribution \(S=5.58 with 11 processors; see Fig.16\).)show
233 79 gm
1.33804 0. 32 0.13380 0.(Our results can easily be compared with results obtained by other researchers. For instance, in)awidthshow
244 79 gm
0.79193 0. 32 0.07919 0.([MOS86] a speedup of 3.66 with 5 workstations is reported; such a measure was obtained with a)awidthshow
255 79 gm
0.22323 0. 32 0.02232 0.(depth of 7 plies on the Bratko-Kopec test; with a shallower depth \(5 plies\) we got a speedup of 3.49)awidthshow
266 79 gm
1.10260 0. 32 0.11026 0.(\(3.75 with score sharing\). In [Sch89] a speedup of 4.78 with 7 processors, depth of 7 plies was)awidthshow
277 79 gm
0.07385 0. 32 0.00738 0.(obtained for DPVSplit; we got a speedup of 4.54 \(depth = 5 plies\). These results seem to say that the)awidthshow
288 79 gm
1.30981 0. 32 0.13098 0.(use of the Linda programming model does not introduce any special overhead for this class of)awidthshow
299 79 gm
(programs.)show
310 79 gm
0.55175 0. 32 0.05517 0.(On the other hand, we got bad comparison results for algorithms based on dynamic distribution of)awidthshow
321 79 gm
2.16812 0. 32 0.21681 0.(search. However, the problem seems to be the hardware architecture, not the programming)awidthshow
332 79 gm
(environment; in fact, we found the following results in literature:)show
345 88 gm
10 fz
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2 F /|______Times-Roman fnt
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0.34454 0. 32 0.03445 0.(\245\312[Eli90] reports that the program Oracol, based on dynamic splitting and written in Orca, gets a maximum)awidthshow
356 101 gm
(speedup of 5.5 on a multiprocessor with shared memory and 10 processors.)show
369 88 gm
1.61331 0. 32 0.16133 0.(\245\312[FMM92] presents a dynamic algorithm based on "young-brothers-wait". On a transputer with 256)awidthshow
380 101 gm
(processors, the authors report a surprising speedup of 126 \(depth 8-plies\).)show
391 79 gm
11 fz
bu fc
2 F /|______Times-Roman fnt
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0.74722 0. 32 0.07472 0.(These results suggest that dynamic splitting algorithms can offer good performances, but only on)awidthshow
402 79 gm
0.29296 0. 32 0.02929 0.(shared memory or on massive parallel systems where communication and fine-grain parallelism are)awidthshow
413 79 gm
0.30899 0. 32 0.03089 0.(cheap. It would be interesting to test out general dynamic splitting algorithm on these architectures.)awidthshow
424 79 gm
1.09130 0. 32 0.10913 0.(Also, it would be interesting to verify in massively parallel machines the asyntotic convergence)awidthshow
435 79 gm
(postulated in [MOS86] for static splitting methods .)show
457 79 gm
1 fs
bu fc
2 F /|______Times-Bold fnt
bn
0.00860 0.(Acknowledgements)ashow
457 170 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
3.80035 0. 32 0.38003 0.(. This paper has been partially supported by ESPRIT BRA Project)awidthshow
468 79 gm
0.03295 0. 32 0.00329 0.(BROADCAST and by Italian CNR.)awidthshow
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91 476 gm
(nc 30 28 811 566 6 rc)kp
F 1 setTxMode
0 fs
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2 F /|______Helvetica fnt
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(Bibliography)show
773 79 gm
(UBLCS-94-14)show
773 514 gm
(18)show
134 79 gm
1 fs
12 fz
bu fc
2 F /|______Times-Bold fnt
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(Bibliography)show
158 79 gm
0 fs
11 fz
bu fc
2 F /|______Times-Roman fnt
bn
0.00982 0.([ABD82])ashow
158 130 gm
0.88424 0. 32 0.08842 0.(S.Akl, D.Barnard, R.Doran, "Design, Analysis, and Implementation of a Parallel Tree)awidthshow
169 130 gm
0.81619 0. 32 0.08161 0.(Search Algorithm", )awidthshow
169 221 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
0.82031 0. 32 0.08203 0.(IEEE Transactions on Pattern Analysis and Machine Intelligence,)awidthshow
180 130 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
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191 79 gm
0.11459 0. 32 0.01145 0.([BalvRe86] H.Bal, R.vanRenesse, "A summary of parallel alpha-beta search results", )awidthshow
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
0.16403 0. 32 0.01640 0.(ICCA Journal)awidthshow
191 520 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
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202 130 gm
(\(Sep.1986\), 146-149.)show
213 79 gm
0.00852 0.([Bau78])ashow
213 130 gm
0.95748 0. 32 0.09574 0.(G.Baudet, "The design and analysis of algorithms for asynchronous multiprocessors",)awidthshow
224 130 gm
(Ph.D. Thesis, CS Dept., Carnegie-Mellon Univ., \(Apr.1978\).)show
235 79 gm
1.93359 0. 32 0.19335 0.([BraKop82] I.Bratko, D.Kopec, "The Bratko-Kopec experiment: a comparison of human and)awidthshow
246 130 gm
1.90719 0. 32 0.19071 0.(computer performance in chess", )awidthshow
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
1.87927 0. 32 0.18792 0.(Advances in Computer Chess 3)awidthshow
0 fs
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bn
1.51840 0. 32 0.15184 0.(, M Clarke \(Ed.\),)awidthshow
257 130 gm
(\(1982\), 57)show
257 175 gm
(-72, Pergamon Press.)show
268 79 gm
0.81268 0. 32 0.08126 0.([CarGel90] N.Carriero, D.Gelernter, )awidthshow
268 247 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
1.04995 0. 32 0.10499 0.(How to write parallel programs. A first course)awidthshow
268 464 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
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279 130 gm
(1990.)show
290 79 gm
([Ebe86])show
290 130 gm
(C.Ebeling, )show
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(All the Right Moves: A VLSI Architecture for Chess)show
290 406 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, MIT Press, 1986.)show
301 79 gm
([Eli90])show
301 130 gm
0.07461 0. 32 0.00746 0.(R.Elias, "Oracol, A Chess Problem Solver in Orca", Dept. of Mathematics and Computer)awidthshow
312 130 gm
(Science, Vrije Universiteit, Amsterdam, \(1990\).)show
323 79 gm
([Elo86])show
323 130 gm
(A.Elo, The Rating of Chessplayers: Past and Present, 2nd Ed., Arco, 1986.)show
334 79 gm
0.01040 0.([FMM91])ashow
334 130 gm
0.47592 0. 32 0.04759 0.(R.Feldmann, P.Mysliwietz, B.Monien, "A Fully Distributed Chess Program", )awidthshow
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
0.12760 0.(Advances)ashow
345 130 gm
(in computer chess)show
345 209 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
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345 330 gm
(-27.)show
356 79 gm
0.01040 0.([FMM92])ashow
356 130 gm
1.51596 0. 32 0.15159 0.(R.Feldmann, P.Mysliwietz, B.Monien, "Experiments with a Fully-Distributed Chess)awidthshow
367 130 gm
1.80343 0. 32 0.18034 0.(Program", )awidthshow
367 181 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
1.83212 0. 32 0.18321 0.(Heuristic Programming in AI)awidthshow
367 321 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
1.69158 0. 32 0.16915 0.(, J.VanDenHerik and\312V.Allis \(Eds.\), Hellis)awidthshow
378 130 gm
(Horwood, \(1992\), 72-87.)show
389 79 gm
0.00732 0.([FelOtt88])ashow
389 130 gm
2.39242 0. 32 0.23924 0.(E.Felten, S.Otto, "A Highly Parallel Chess Program", )awidthshow
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
2.52624 0. 32 0.25262 0.(Proc. of the International)awidthshow
400 130 gm
(Conference on Fifth Generation Computer Systems)show
400 356 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
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(, \(1988\), 1001-1009.)show
411 79 gm
0.00732 0.([FisFin80])ashow
411 130 gm
0.42098 0. 32 0.04209 0.(J.Fishburn, R.Finkel, "Parallelism in Alpha-Beta Search on Arachne", Technical Report)awidthshow
422 130 gm
(394, CS. Dept., Univ. of Wisconsin, Madison, \(Jul.1980\).)show
433 79 gm
0.00732 0.([FinFis82])ashow
433 130 gm
0.40954 0. 32 0.04095 0.(J.Fishburn, R.Finkel, "Parallelism in alpha-beta search", )awidthshow
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
0.57022 0. 32 0.05702 0.(Artificial Intelligence)awidthshow
433 479 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
0.62805 0. 32 0.06280 0.(, Vol. 19,)awidthshow
444 130 gm
(\(1982\), 89)show
444 175 gm
(-106.)show
455 79 gm
0.21102 0. 32 0.02110 0.([FMMV89] R.Feldmann, P.Mysliwietz, B.Monien, O.Vornberger, "Distributed Game-Tree Search",)awidthshow
466 130 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
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(ICCA Journal)show
466 192 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, Vol.12, No.2, \(1989\), 65-73.)show
477 79 gm
([Gil72])show
477 130 gm
1.13174 0. 32 0.11317 0.(J.Gillogly, "The Technology Chess Program", )awidthshow
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
1.52526 0. 32 0.15252 0.(Artificial Intelligence)awidthshow
477 445 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
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1.66229 0. 32 0.16622 0.(, Vol. 3, \(1972\),)awidthshow
488 130 gm
(145-163.)show
499 79 gm
0.00852 0.([Hsu90])ashow
499 130 gm
0.22567 0. 32 0.02256 0.(F.Hsu, "Large scale parallelization of alpha)awidthshow
499 323 gm
0.22186 0. 32 0.02218 0.(-beta search: an algorithmic and architectural)awidthshow
510 130 gm
0.32073 0. 32 0.03207 0.(study with computer chess", Ph.D. thesis, Carnegie Mellon University, Pittsburgh, \(Feb.)awidthshow
521 130 gm
(1990\).)show
532 79 gm
0.00939 0.([SCA90])ashow
532 130 gm
2.24731 0. 32 0.22473 0.("C-Linda Reference Manual", Scientific Computing Associates Inc., New Haven,)awidthshow
543 130 gm
(Connecticut, \(1990\).)show
554 79 gm
0.00982 0.([MBS91])ashow
554 130 gm
1.20208 0. 32 0.12020 0.(T.Marsland, T.Breitkreutz, S.Sutphen, \322A network multiprocessor for experiments in)awidthshow
565 130 gm
(parallelism\323, )show
565 189 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
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(Concurrency: Practice and Experience)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, 3\(3\), \(Jun.1991\), 203-219.)show
576 79 gm
0.81314 0. 32 0.08131 0.([MarCam82] T.Marsland, M.Campbell, "Parallel Search of Strongly Ordered Game Trees", )awidthshow
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
0.43041 0.(ACM)ashow
587 130 gm
(Computing Surveys)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, Vol.14, No.4, \(Dec.1982\), 533-551.)show
598 79 gm
0.00996 0.([MOS86])ashow
598 130 gm
3.57879 0. 32 0.35787 0.(T.Marsland, M.Olafsson,J.Schaeffer, "Multiprocessor tree-search experiments",)awidthshow
609 130 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
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(Adavances in Computer Chess 4)show
609 273 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, Pergamon Press, \(1986\), 37-51.)show
620 79 gm
([Sch89])show
620 130 gm
1.27441 0. 32 0.12744 0.(J.Schaeffer, "Distributed Game-Tree Searching", )awidthshow
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
1.08673 0. 32 0.10867 0.(Journal of Parallel and Distributed)awidthshow
631 130 gm
(Computing)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, 6, \(1989\), 90-114.)show
642 79 gm
([Sti91])show
642 130 gm
3.38684 0. 32 0.33868 0.(L.Stiller, "Group Graphs and Computational Symmetry on Massively Parallel)awidthshow
653 130 gm
(Architecture", )show
653 195 gm
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
(The Journal of Supercomputing)show
0 fs
bu fc
2 F /|______Times-Roman fnt
bn
(, 5, \(1991\), 99-117.)show
664 79 gm
0.00852 0.([Tho82])ashow
664 130 gm
1.79061 0. 32 0.17906 0.(K.Thompson, "Computer Chess Strength", )awidthshow
2 fs
bu fc
2 F /|______Times-Italic fnt
bn
1.52160 0. 32 0.15216 0.(Advances in Computer Chess 3)awidthshow
664 481 gm
0 fs
bu fc
2 F /|______Times-Roman fnt
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1.78756 0. 32 0.17875 0.(, M.R.B.)awidthshow
675 130 gm
(Clarke \(Ed.\), Pergamon Press, \(1982\), 55-56.)show
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