Parallel Search, also known as Multithreaded Search or SMP Search, is a way to increase search speed by using additional processors. This topic that has been gaining popularity recently with multiprocessor computers becoming widely available. Utilizing these additional processors is an interesting domain of research, as traversing a search tree is inherently serial. Several approaches have been devised, with the most popular today being Young Brothers Wait Concept and Shared Hash Table.

This page gives a brief summary of the different types. SMP algorithms are classified by their scalability (trend in search speed as the number of processors becomes large) and their speedup (change in time to complete a search). Typically, programmers use scaling to mean change in nodes per second (NPS) rates, and speedup to mean change in time to depth. Scaling and scalability are thus two different concepts.

This technique is a very simple approach to SMP. The implementation requires little more than starting additional processors. Processors are simply fed the root position at the beginning of the search, and each searches the same tree with the only communication being the transposition table. The gains come from the effect of nondeterminism. Each processor will finish the various subtrees in varying amounts of time, and as the search continues, these effects grow making the search trees diverge. The speedup is then based on how many nodes the main processor is able to skip from transposition table entries. Many programs used this if a "quick and dirty" approach to SMP is needed. It had the reputation of little speedup on a mere 2 processors, and to scale quite badly after this.

Lazy SMP

Recent improvements by Dan Homan^{[2]} , Martin Sedlak^{[3]} and others on Lazy SMP indicate that the algorithm scales quite well up to 8 cores and beyond ^{[4]} .

ABDADA, Alpha-Bêta Distribué avec Droit d'Aînesse (Distributed Alpha-Beta Search with Eldest Son Right) is a loosely synchronized, distributed search algorithm by Jean-Christophe Weill^{[5]} . It is based on the Shared Hash Table, and adds the number of processors searching this node inside the hash-table entry for better utilization - considering the Young Brothers Wait Concept.

Parallel Alpha-Beta

These algorithms divide the Alpha-Beta tree, giving different subtrees to different processors. Because alpha-beta is a serial algorithm, this approach is much more complex. However, these techniques also provide for the greatest gains from additional processors.

Principal Variation Splitting (PVS)

In Principal Variation Splitting (PVS), each node is expressed by a thread. A thread will spawn one child thread for each legal move. But data dependency specified by the algorithm exists among these threads: After getting a tighter bound from the thread corresponding to the PV node, the remaining threads are ready to run.

PV Splitting ^{[6]}

YBWC and Jamboree

The idea in Feldmann'sYoung Brothers Wait Concept (YBWC) ^{[7]}^{[8]} as well in Kuszmaul'sJamboree Search^{[9]}^{[10]}^{[11]} , is to search the first sibling node first before spawning the remaining siblings in parallel. This is based on the observations that the first move is either going to produce a cutoff (in which case processing sibling nodes is wasted effort) or return much better bounds. If the first move does not produce a cut-off, then the remaining moves are searched in parallel. This process is recursive.

Since the number of processors is not infinite the process of "spawning" work normally consists in putting it on some kind of "work to be done stack" where processors are free to grab work in FIFO fashion when there is no work to do. In YBW you would not "spawn" or place work on the stack until the first sibling is searched.

In their 1983 paper Improved Speedup Bounds for Parallel Alpha-Beta Search^{[12]} , Raphael Finkel and John Philip Fishburn already gave the theoretical confirmation to the common sense wisdom that parallel resources should first be thrown into searching the first child. Assuming the tree is already in an approximation to best-first order, this establishes a good alpha value that can then be used to parallel search the later children. The algorithm in the 1982 Artificial Intelligence paper ^{[13]} , which Fishburn called the "dumb algorithm" in his 1981 thesis presentation ^{[14]} gives p^0.5 speedup with p processors, while the 1983 PAMI algorithm (the "smart algorithm") gives p^0.8 speedup for lookahead trees with the branching factor of chess.

This algorithm, invented by the Cray Blitz team (including Robert Hyatt^{[15]} ), is the most complex. Though this gives the best known scalability for any SMP algorithm, there are very few programs using it because of its difficulty of implementation.

Other Approaches

Many different approaches have been tried that do not directly split the search tree. These algorithms have not enjoyed popular success due to the fact that they are not scalable. Typical examples include one processor that evaluates positions fed to it by a searching processor, or a tactical search that confirms or refutes a positional search.

In 1994, Robert Hyatt^{[19]} reported some scaling comparisons of different Parallel Search algorithms. The values indicate the speedup to solve certain testpositions with n processors.

Algorithm

1

2

4

8

16

PVS

1.0

1.8

3.0

4.1

4.6

EPVS

1.0

1.9

3.4

5.4

6.0

DTS

1.0

2.0

3.7

6.6

11.1

Other Considerations

Semaphores

During an parallel search, certain areas of memory must be protected to make sure processors do not write simultaneously and corrupt the data. Some type of semaphore system must be used. Semaphores access a piece of shared memory, typically an integer. When a processor wants to access protected memory, it reads the integer. If it is zero, meaning no other process is accessing the memory, then the processor attempts to make the integer nonzero. This whole process must be done atomically, meaning that the read, compare, and write are all done at the same time. Without this atomicity another processor could read the integer at the same time and both would see that they can freely access the memory.

In chess programs that use parallel alpha-beta, usually spinlocks are used. Because the semaphores are held for such short periods of time, processors want to waste as little time as possible after the semaphore is released before acquiring access. To do this, if the semaphore is held when a processor reaches it, the processor continuously reads the semaphore. This technique can waste a lot of processing time in applications with high contention, meaning that many processes try to access the same semaphore simultaneously. In chess programs, however, we want as much processing power as possible.

Spinlocks are sometimes implemented in assembly language because the operating system does not have an API for them.

Threads vs. Processes

There are two ways of utilizing the extra processing power of multiple CPUs, threads and processes. The difference between them is that threads share all memory in the program, but there are multiple threads of execution. In processes, all memory is local to each processor except memory that is explicitly shared. This means that in a threaded program, functions must pass around an extra argument specifying which thread is active, thus which board structure to use. When using processes, a single global board can be used that will be duplicated for each process.

Threads are more common, because they are easier to debug as well as implement, provided the program does not already have lots of global variables. Processes are favored by some because the need to explicitly share memory makes subtle bugs easier to avoid. Also, in processes, the extra argument to most functions is not needed.

Selim Akl, David T. Barnard, R.J. Doran, (1980). Design, analysis and implementation of a parallel alpha-beta algorithm, Department of Computing and Information Science, Queen's University, Kingston, Ontario.

Selim Akl, David T. Barnard, R.J. Doran (1980). Simulation and Analysis in Deriving Time and Storage Requirements for a Parallel Alpha-Beta Pruning Algorithm. IEEE International Conference on Parallel Processing, pp. 231-234.

Selim Akl, David T. Barnard, R.J. Doran (1980). Searching game trees in parallel, Proceedings of the Third Biennial Conference of the Canadian Society for Computational Studies of Intelligence, Victoria, B.C.

1981

John Philip Fishburn (1981). Analysis of Speedup in Distributed Algorithms. Ph.D. Thesis, pdf

Selim Akl, R.J. Doran (1981). A comparison of parallel implementations of the alpha-beta and Scout tree search algorithms using the game of checkers, Department of Computing and Information Science, Queen's University, Kingston, Ontario.

Jonathan Schaeffer (1988). Distributed Game-Tree Searching. Journal of Parallel and Distributed Computing, Vol. 6, No. 2, pp. 90-114.

Chris Ferguson, Richard Korf (1988). Distributed Tree Search and its Application to Alpha-Beta Pruning. Proceedings of AAAI-88, Vol. I, pp. 128-132. Saint Paul, MN, pdf

Monroe Newborn (1988). Unsynchronized Iterative Deepening Parallel Alpha-Beta Search. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI, Vol. 10, No. 5, pp. 687-694. ISSN 0162-8828.

Robert Hyatt, Bruce W. Suter, Harry Nelson (1989). A Parallel Alpha-Beta Tree Searching Algorithm. Parallel Computing, Vol. 10, No. 3, pp. 299-308. ISSN 0167-8191.

Feng-hsiung Hsu (1989). Large Scale Parallelization of Alpha-beta Search: An Algorithmic and Architectural Study with Computer Chess. Ph.D. thesis, Technical report CMU-CS-90-108, Carnegie Mellon University, advisor Hsiang-Tsung Kung

Rainer Feldmann, Peter Mysliwietz, Burkhard Monien (1992). Distributed Game Tree Search on a Massively Parallel System. Data Structures and Efficient Algorithms, B. Monien, Th. Ottmann (eds.), Springer, Lecture Notes in Computer Science, 594, 1992, 270-288

1993

Rainer Feldmann (1993). Game Tree Search on Massively Parallel Systems. Ph.D. Thesis, pdf

Florian Schintke, Jens Simon, Alexander Reinefeld (2001). A Cache Simulator for Shared Memory Systems. International Conference on Computational Science ICCS 2001, San Francisco, CA, Springer LNCS 2074, vol. 2, pp. 569-578. zipped ps

2002

Akihiro Kishimoto, Jonathan Schaeffer. (2002). Distributed Game-Tree Search Using Transposition Table Driven Work Scheduling, In Proc. of 31st International Conference on Parallel Processing (ICPP'02), pages 323-330, IEEE Computer Society Press. pdf via CiteSeerX

Akihiro Kishimoto, Jonathan Schaeffer. (2002). Transposition Table Driven Work Scheduling in Distributed Game-Tree Search (Best Paper Prize), In Proc. of Fifteenth Canadian Conference on Artificial Intelligence (AI'2002), volume 2338 of Lecture Notes in Artificial Intelligence (LNAI), pages 56-68, Springer

^John Romein, Henri Bal, Jonathan Schaeffer, Aske Plaat (2002). A Performance Analysis of Transposition-Table-Driven Scheduling in Distributed Search. IEEE Transactions on Parallel and Distributed Systems, Vol. 13, No. 5, pp. 447–459. pdf

Home * Search * Parallel SearchParallel Search, also known asMultithreaded Searchor SMP Search, is a way to increase search speed by using additional processors. This topic that has been gaining popularity recently with multiprocessor computers becoming widely available. Utilizing these additional processors is an interesting domain of research, as traversing a search tree is inherently serial. Several approaches have been devised, with the most popular today being Young Brothers Wait Concept and Shared Hash Table.This page gives a brief summary of the different types. SMP algorithms are classified by their scalability (trend in search speed as the number of processors becomes large) and their speedup (change in time to complete a search). Typically, programmers use

scalingto mean change in nodes per second (NPS) rates, and speedup to mean change in time to depth. Scaling and scalability are thus two different concepts.A subtype of parallel algorithms, distributed algorithms are algorithms designed to work in cluster computing and distributed computing environments, where additional concerns beyond the scope of "classical" parallel algorithms need to be addressed.

^{[1]}## Table of Contents

## Shared Hash Table

see Main page: Shared Hash TableThis technique is a very simple approach to SMP. The implementation requires little more than starting additional processors. Processors are simply fed the root position at the beginning of the search, and each searches the same tree with the only communication being the transposition table. The gains come from the effect of nondeterminism. Each processor will finish the various subtrees in varying amounts of time, and as the search continues, these effects grow making the search trees diverge. The speedup is then based on how many nodes the main processor is able to skip from transposition table entries. Many programs used this if a "quick and dirty" approach to SMP is needed. It had the reputation of little speedup on a mere 2 processors, and to scale quite badly after this.

## Lazy SMP

Recent improvements by Dan Homan^{[2]}, Martin Sedlak^{[3]}and others onLazySMP indicate that the algorithm scales quite well up to 8 cores and beyond^{[4]}.## ABDADA

see Main page: ABDADAABDADA, Alpha-Bêta Distribué avec Droit d'Aînesse (Distributed Alpha-Beta Search with Eldest Son Right) is a loosely synchronized, distributed search algorithm by Jean-Christophe Weill

^{[5]}. It is based on the Shared Hash Table, and adds the number of processors searching this node inside the hash-table entry for better utilization - considering the Young Brothers Wait Concept.## Parallel Alpha-Beta

These algorithms divide the Alpha-Beta tree, giving different subtrees to different processors. Because alpha-beta is a serial algorithm, this approach is much more complex. However, these techniques also provide for the greatest gains from additional processors.## Principal Variation Splitting (PVS)

In Principal Variation Splitting (PVS), each node is expressed by a thread. A thread will spawn one child thread for each legal move. But data dependency specified by the algorithm exists among these threads: After getting a tighter bound from the thread corresponding to the PV node, the remaining threads are ready to run.^{[6]}## YBWC and Jamboree

The idea in Feldmann's Young Brothers Wait Concept (YBWC)^{[7]}^{[8]}as well in Kuszmaul's Jamboree Search^{[9]}^{[10]}^{[11]}, is to search the first sibling node first before spawning the remaining siblings in parallel. This is based on the observations that the first move is either going to produce a cutoff (in which case processing sibling nodes is wasted effort) or return much better bounds. If the first move does not produce a cut-off, then the remaining moves are searched in parallel. This process is recursive.Since the number of processors is not infinite the process of "spawning" work normally consists in putting it on some kind of "work to be done stack" where processors are free to grab work in FIFO fashion when there is no work to do. In YBW you would not "spawn" or place work on the stack until the first sibling is searched.

In their 1983 paper

Improved Speedup Bounds for Parallel Alpha-Beta Search^{[12]}, Raphael Finkel and John Philip Fishburn already gave the theoretical confirmation to the common sense wisdom that parallel resources should first be thrown into searching the first child. Assuming the tree is already in an approximation to best-first order, this establishes a good alpha value that can then be used to parallel search the later children. The algorithm in the 1982 Artificial Intelligence paper^{[13]}, which Fishburn called the "dumb algorithm" in his 1981 thesis presentation^{[14]}gives p^0.5 speedup with p processors, while the 1983 PAMI algorithm (the "smart algorithm") gives p^0.8 speedup for lookahead trees with the branching factor of chess.## Dynamic Tree Splitting (DTS)

Main page: Dynamic Tree SplittingThis algorithm, invented by the Cray Blitz team (including Robert Hyatt

^{[15]}), is the most complex. Though this gives the best known scalability for any SMP algorithm, there are very few programs using it because of its difficulty of implementation.## Other Approaches

Many different approaches have been tried that do not directly split the search tree. These algorithms have not enjoyed popular success due to the fact that they are not scalable. Typical examples include one processor that evaluates positions fed to it by a searching processor, or a tactical search that confirms or refutes a positional search.## Taxonomy

Overview and taxonomy of parallel algorithms based on alpha-beta, given by Mark Brockington, ICCA Journal, Vol. 19: No. 3 in 1996^{[16]}Described

Control Distribution

At These Nodes

At These Nodes

Leftmost child of 3

John Philip Fishburn

Murray Campbell

Leftmost child of 3

^{[17]}Bruce W. Suter,

Harry Nelson

Steve Otto

with no TT-Entry

& no cutoff

Richard Korf

Tree Expansion

^{[18]}Yaoqing Gao

Jonathan Schaeffer

## Comparison

In 1994, Robert Hyatt^{[19]}reported some scaling comparisons of different Parallel Search algorithms. The values indicate the speedup to solve certain testpositions with n processors.## Other Considerations

## Semaphores

During an parallel search, certain areas of memory must be protected to make sure processors do not write simultaneously and corrupt the data. Some type of semaphore system must be used. Semaphores access a piece of shared memory, typically an integer. When a processor wants to access protected memory, it reads the integer. If it is zero, meaning no other process is accessing the memory, then the processor attempts to make the integer nonzero. This whole process must be done atomically, meaning that the read, compare, and write are all done at the same time. Without this atomicity another processor could read the integer at the same time and both would see that they can freely access the memory.In chess programs that use parallel alpha-beta, usually spinlocks are used. Because the semaphores are held for such short periods of time, processors want to waste as little time as possible after the semaphore is released before acquiring access. To do this, if the semaphore is held when a processor reaches it, the processor continuously reads the semaphore. This technique can waste a lot of processing time in applications with high contention, meaning that many processes try to access the same semaphore simultaneously. In chess programs, however, we want as much processing power as possible.

Spinlocks are sometimes implemented in assembly language because the operating system does not have an API for them.

## Threads vs. Processes

There are two ways of utilizing the extra processing power of multiple CPUs, threads and processes. The difference between them is that threads share all memory in the program, but there are multiple threads of execution. In processes, all memory is local to each processor except memory that is explicitly shared. This means that in a threaded program, functions must pass around an extra argument specifying which thread is active, thus which board structure to use. When using processes, a single global board can be used that will be duplicated for each process.Threads are more common, because they are easier to debug as well as implement, provided the program does not already have lots of global variables. Processes are favored by some because the need to explicitly share memory makes subtle bugs easier to avoid. Also, in processes, the extra argument to most functions is not needed.

Some programs that use threads:

^{[20]}^{[21]}Some programs that use processes:

## Didactic Programs

## See also

## Publications

## 1950 ...

1958).Parallel Programming. The Computer Journal, Vol. 1, No. 1## 1970 ...

1978).The Design and Analysis of Algorithms for Asynchronous Multiprocessors. Ph.D. thesis, Carnegie Mellon University, advisor Hsiang-Tsung Kung## 1980 ...

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2000).The Multigame Reference Manual. Vrije Universiteit, pdf20012001).Multigame - An Environment for Distributed Game-Tree Search. Ph.D. thesis, Vrije Universiteit, supervisor Henri Bal, pdf2001).Parallel randomized best-first minimax search. School of Computer Science, Tel-Aviv University, pdf2001).Parallel Alpha-Beta Search on Shared Memory Multiprocessors. Masters Thesis, pdf Copyright © 2001 by Valavan Manohararajah2001).A Cache Simulator for Shared Memory Systems. International Conference on Computational Science ICCS 2001, San Francisco, CA, Springer LNCS 2074, vol. 2, pp. 569-578. zipped ps20022002).Distributed Game-Tree Search Using Transposition Table Driven Work Scheduling, In Proc. of 31st International Conference on Parallel Processing (ICPP'02), pages 323-330, IEEE Computer Society Press. pdf via CiteSeerX2002).Transposition Table Driven Work Scheduling in Distributed Game-Tree Search(Best Paper Prize), In Proc. of Fifteenth Canadian Conference on Artificial Intelligence (AI'2002), volume 2338 of Lecture Notes in Artificial Intelligence (LNAI), pages 56-68, Springer2002).A Performance Analysis of Transposition-Table-Driven Scheduling in Distributed Search. IEEE Transactions on Parallel and Distributed Systems, Vol. 13, No. 5, pp. 447–459. pdf » Transposition Table^{[27]}2002).Nagging: A Scalable Fault-Tolerant Paradigm for Distributed Search. Artificial Intelligence 140, pdf, pdf20032003).Parallelizing a Simple Chess Program. pdf20042004).Parallel Chess Searching and Bitboards. Masters Thesis, postscript## 2005 ...

2005).Transposition-Driven Scheduling in Parallel Two-Player State-Space Search. Masters Thesis, pdf20062006).The Problem with Threads. Technical Report No. UCB/EECS-2006-1, University of California, Berkeley, pdf20072007).The Method of the Chess Search Algorithms - Parallelization using Two-Processor distributed System, pdf2007).On the Parallelization of UCT. CGW 2007, pdf » UCT2007).Multiple Parallel Search in Shogi. 12th Game Programming Workshop20082008).Parallel Monte-Carlo Tree Search. CG 2008, pdf2008).A Parallel Monte-Carlo Tree Search Algorithm. CG 2008, pdf2008).The Parallelization of Monte-Carlo Planning - Parallelization of MC-Planning. ICINCO-ICSO 2008: 244-249, pdf, slides as pdf2008).A Twofold Distributed Game-Tree Search Approach Using Interconnected Clusters. Euro-Par 2008: 587-598, abstract from springerlink2008).A Parallel Monte-Carlo Tree Search Algorithm. pdf20092009).A lock-free multithreaded Monte-Carlo tree search algorithm, Advances in Computer Games 12, pdf2009).Parallel Heuristic Search. In: C.A. Floudas, P.M. Pardalos (eds.), Encyclopedia of Optimization 2nd ed. pp 2908-29122009).Parallel Nested Monte-Carlo Search. NIDISC 2009, pdf2009).Aggrandizement of Board Games’ Performance on Multi-core Systems: Taking GNU-Chess as a prototype. BMS College of Engineering, Faculty mentor: Professor Ashok Kumar, Intel® Developer Zone » GNU Chess## 2010 ...

2010).Scalability and Parallelization of Monte-Carlo Tree Search. CG 2010, pdf2010).Parallel Alpha-Beta Based Game Tree Search, slides as pdf2010).Implementation of Parallel Game Tree Search on a SIMD System. Huazhong University of Science & Technology, Wuhan, China, ICIE 2010, Vol. 12010).Parallel Depth First Proof Number Search. AAAI 2010 » Proof-Number Search20112011).A Parallel General Game Player. KI Journal, Vol. 25, No. 1, pdf2011).Scalable Distributed Monte Carlo Tree Search. SoCS2011, pdf2011).Parallel Game Tree Search Using GPU. Institute of Informatics and Software Engineering, Faculty of Informatics and Information Technologies, Slovak University of Technology in Bratislava, pdf » GPU2011).A Distributed Chess Playing Software System Model Using Dynamic CPU Availability Prediction. SERP 2011, pdf2011).Shared-memory Parallel Programming with Cilk. Rice University, slides as pdf » Cilk2011).UCT-Treesplit - Parallel MCTS on Distributed Memory. MCTS Workshop, Freiburg, Germany, pdf » UCT2011).Parallel Monte-Carlo Tree Search for HPC Systems. Euro-Par 2011, pdf20122012).Volunteer Computing System Applied to Computer Games. TCGA 2012 Workshop, pdf20132013).Parallel Dovetailing and its Application to Depth-First Proof-Number Search. ICGA Journal, Vol. 36, No. 1 » Proof-Number Search^{[28]}2013).Scalable Parallel DFPN Search. CG 201320142014).Is Parallel Programming Hard, And, If So, What Can You Do About It?. pdf2014).Parallel Monte-Carlo Tree Search for HPC Systems and its Application to Computer Go. Ph.D. thesis, University of Paderborn, advisors Marco Platzner, Ulf Lorenz, pdf, pdf2014).Performance analysis of a 240 thread tournament level MCTS Go program on the Intel Xeon Phi. CoRR abs/1409.4297 » Go, MCTS, x86-64## 2015 ...

2015).Feature Strength and Parallelization of Sibling Conspiracy Number Search. Advances in Computer Games 142015).Parameter-Free Tree Style Pipeline in Asynchronous Parallel Game-Tree Search. Advances in Computer Games 142015).Scaling Monte Carlo Tree Search on Intel Xeon Phi. CoRR abs/1507.04383 » Hex, MCTS, x86-642015).Parallel Monte Carlo Tree Search from Multi-core to Many-core Processors. TrustCom/BigDataSE/|ISPA 2015, pdf## Forum Posts

## 1995 ...

## 2000 ...

## 2005 ...

Results from UCT parallelization by Gian-Carlo Pascutto, CCC, March 11, 2009

## 2010 ...

201120122013^{[29]}^{[30]}Measure of SMP scalability (sub-thread) by Ernest Bonnem, CCC, July 08, 2013

2014## 2015 ...

Explanation for non-expert? by Louis Zulli, CCC, February 16, 2015 » Stockfish

Best Stockfish NPS scaling yet by Louis Zulli, CCC, March 02, 2015

^{[31]}2016## External Links

## Parallel Search

## Parallel Computing

## Scalability

## Shared Memory

## Cache

MSI protocol from Wikipedia

MESI protocol from Wikipedia

MOESI protocol from Wikipedia

assembly - The prefetch instruction - Stack Overflow

Data Prefetch Support - GNU Project - Free Software Foundation (FSF)

Software prefetching considered harmful by Linus Torvalds, LWN.net, May 19, 2011

## Concurrency and Synchronization

Cooperating sequential processes (EWD 123)

A challenge to memory designers? (EWD 497)

## Misc

## References

1996).The ABDADA Distributed Minimax Search Agorithm. Proceedings of the 1996 ACM Computer Science Conference, pp. 131-138. ACM, New York, N.Y, reprinted ICCA Journal, Vol. 19, No. 1, zipped postscript1996).Multithreaded Pruned Tree Search in Distributed Systems. Journal of Computing and Information, 2(1), 482-492, pdf1991).A Fully Distributed Chess Program. Advances in Computer Chess 6, pdf1993).Game Tree Search on Massively Parallel Systems. Ph.D. Thesis, pdf1994).Massively Parallel Chess, pdf1994).Synchronized MIMD Computing. Ph. D. Thesis, Massachusetts Institute of Technology, pdf1995).The StarTech Massively Parallel Chess Program. pdf1983).Improved Speedup Bounds for Parallel Alpha-Beta Search. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 5, No. 1, pp. 89 - 921982).Parallelism in Alpha-Beta Search. Artificial Intelligence, Vol. 19, No. 11981).Analysis of Speedup in Distributed Algorithms. Ph.D. Thesis, pdf1994).The DTS high-performance parallel tree search algorithm1996).A Taxonomy of Parallel Game-Tree Search Algorithms. ICCA Journal, Vol. 19: No. 31994).The DTS high-performance parallel tree search algorithm1985).Lionel Moser: An Experiment in Distributed Game Tree Searching.ICCA Journal, Vol. 8, No. 2 (Review)2002).A Performance Analysis of Transposition-Table-Driven Scheduling in Distributed Search. IEEE Transactions on Parallel and Distributed Systems, Vol. 13, No. 5, pp. 447–459. pdf## What links here?

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