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Nearly Optimal Minimax Tree Search?
, 1994
"... Knuth and Moore presented a theoretical lower bound on the number of leaves that any fixeddepth minimax treesearch algorithm traversing a uniform tree must explore, the socalled minimal tree. Since reallife minimax trees aren't uniform, the exact size of this tree isn't known for most applicatio ..."
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Cited by 15 (11 self)
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Knuth and Moore presented a theoretical lower bound on the number of leaves that any fixeddepth minimax treesearch algorithm traversing a uniform tree must explore, the socalled minimal tree. Since reallife minimax trees aren't uniform, the exact size of this tree isn't known for most applications. Further, most games have transpositions, implying that there exists a minimal graph which is smaller than the minimal tree. For three games (chess, Othello and checkers) we compute the size of the minimal tree and the minimal graph. Empirical evidence shows that in all three games, enhanced AlphaBeta search is capable of building a tree that is close in size to that of the minimal graph. Hence, it appears gameplaying programs build nearly optimal search trees. However, the conventional definition of the minimal graph is wrong. There are ways in which the size of the minimal graph can be reduced: by maximizing the number of transpositions in the search, and generating cutoffs using bran...
A Performance Analysis of TranspositionTableDriven Scheduling in Distributed Search
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 2002
"... This paper discusses a new workscheduling algorithm for parallel search of singleagent state spaces, called TranspositionTableDriven Work Scheduling, that places the transposition table at the heart of the parallel work scheduling. The scheme results in less synchronization overhead, less proce ..."
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Cited by 11 (6 self)
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This paper discusses a new workscheduling algorithm for parallel search of singleagent state spaces, called TranspositionTableDriven Work Scheduling, that places the transposition table at the heart of the parallel work scheduling. The scheme results in less synchronization overhead, less processor idle time, and less redundant search effort. Measurements on a 128processor parallel machine show that the scheme achieves closetolinear speedups; for large problems the speedups are even superlinear due to better memory usage. On the same machine, the algorithm is 1.6 to 12.9 times faster than traditional workstealingbased schemes.
Transposition Table Driven Work Scheduling in Distributed Search
 IN 16TH NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI'99
, 1999
"... This paper introduces a new scheduling algorithm for parallel singleagent search, transposition table driven work scheduling, that places the transposition table at the heart of the parallel work scheduling. The scheme results in less synchronization overhead, less processor idle time, and less ..."
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Cited by 8 (0 self)
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This paper introduces a new scheduling algorithm for parallel singleagent search, transposition table driven work scheduling, that places the transposition table at the heart of the parallel work scheduling. The scheme results in less synchronization overhead, less processor idle time, and less redundant search effort. Measurements on a 128processor parallel machine show that the scheme achieves nearlyoptimal performance and scales well. The algorithm performs a factor of 2.0 to 13.7 times better than traditional workstealingbased schemes.
A Minimax Algorithm Better than AlphaBeta? No and Yes
, 1995
"... This paper has three main contributions to our understanding of fixeddepth minimax search: (A) A new formulation for Stockman's SSS* algorithm, based on AlphaBeta, is presented. It solves all the perceived drawbacks of SSS*, finally transforming it into a practical algorithm. In effect, we show th ..."
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Cited by 7 (3 self)
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This paper has three main contributions to our understanding of fixeddepth minimax search: (A) A new formulation for Stockman's SSS* algorithm, based on AlphaBeta, is presented. It solves all the perceived drawbacks of SSS*, finally transforming it into a practical algorithm. In effect, we show that SSS* = ab + transposition tables. The crucial step is the realization that transposition tables contain socalled solution trees, structures that are used in bestfirst search algorithms like SSS*. Having created a practical version, we present performance measurements with tournament gameplaying programs for three different minimax games, yielding results that contradict a number of publications. (B) Based on the insights gained in our attempts at understanding SSS*, we present a framework that facilitates the construction of several bestfirst fixeddepth gametree search algorithms, known and new. The framework is based on depthfirst nullwindow AlphaBeta search, enhanced with stora...
Asserting the utility of CO2P3S using the Cowichan problems
, 2002
"... Parallel programming environments provide a way for programmers to reap the benefits of parallelism, while reducing the effort required to create parallel applications. The CO2P3S parallel programming system is one such tool that uses a patternbased approach to express concurrency. Using the Cowich ..."
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Cited by 5 (1 self)
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Parallel programming environments provide a way for programmers to reap the benefits of parallelism, while reducing the effort required to create parallel applications. The CO2P3S parallel programming system is one such tool that uses a patternbased approach to express concurrency. Using the Cowichan Problems, we demonstrate that CO2P3S contains a rich set of parallel patterns for implementing a wide variety of applications running on sharedmemory or distributedmemory hardware. An example of these parallel patterns, the SearchTree pattern, is described and it is shown how the pattern was used to solve the Fifteen Puzzle problem. Code metrics and performance results are presented for the Cowichan applications to show the usability of the CO2P3S system and its ability to reduce programming effort, while producing programs with reasonable performance.
Parallel Randomized BestFirst Minimax Search
, 2001
"... We describe a novel parallel randomized search algorithm for twoplayer games. The algorithm is a randomized version of Korf and Chickering's bestfirst search. Randomization both fixes a defect in the original algorithm and introduces significant parallelism. An experimental evaluation demonstrate ..."
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Cited by 3 (0 self)
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We describe a novel parallel randomized search algorithm for twoplayer games. The algorithm is a randomized version of Korf and Chickering's bestfirst search. Randomization both fixes a defect in the original algorithm and introduces significant parallelism. An experimental evaluation demonstrates that the algorithm is e#cient (in terms of the numb er of searchtree vertices that it visits) and highly parallel. On incremental random game trees the algorithm outperforms AlphaBeta, and speeds upb y a up to a factor of 18 (using 35 processors). In comparison, Jamb oree [Kuszmaul '95], speeds upb y only a factor of 6. The algorithm outperforms AlphaBeta in the game of Othello. We have also evaluated the algorithm in a Chessplaying program using theb oardevaluation code from an existingAlphaBetabfi56 program (Crafty). On a single processor our program is slower than Crafty; with multiple processors it outperforms it.
BestFirst and DepthFirst Minimax Search in Practice
"... Most practitioners use a variant of the AlphaBeta algorithm, a simple depthfirst procedure, for searching minimax trees. SSS*, with its bestfirst search strategy, reportedly offers the potential for more efficient search. However, the complex formulation of the algorithm and its alleged excessive ..."
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Cited by 2 (0 self)
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Most practitioners use a variant of the AlphaBeta algorithm, a simple depthfirst procedure, for searching minimax trees. SSS*, with its bestfirst search strategy, reportedly offers the potential for more efficient search. However, the complex formulation of the algorithm and its alleged excessive memory requirements preclude its use in practice. For two decades, the search efficiency of "smart" bestfirst SSS* has cast doubt on the effectiveness of "dumb" depthfirst AlphaBeta. This paper presents a simple framework for calling AlphaBeta that allows us to create a variety of algorithms, including SSS* and DUAL*. In effect, we formulate a bestfirst algorithm using depthfirst search. Expressed in this framework SSS* is just a special case of AlphaBeta, solving all of the perceived drawbacks of the algorithm. In practice, AlphaBeta variants typically evaluate less nodes than SSS*. A new instance of this framework, MTD(f), outperforms SSS* and NegaScout, the AlphaBeta variant of...
Development and Tuning of Irregular DivideandConquer Applications in DAMPVM/DAC
 In: Recent Advances in Parallel Virtual Machine and Message Passing Interface. Number 2474 in Lecture Notes in Computer Science, SpringerVerlag (2002) 208–216 9th European PVM/MPI Users’ Group Meeting
"... Abstract. This work presents implementations and tuning experiences with parallel irregular applications developed using the object oriented framework DAMPVM/DAC. It is implemented on top of DAMPVM and provides automatic partitioning of irregular divideandconquer (DAC) applications at runtime and ..."
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Cited by 1 (1 self)
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Abstract. This work presents implementations and tuning experiences with parallel irregular applications developed using the object oriented framework DAMPVM/DAC. It is implemented on top of DAMPVM and provides automatic partitioning of irregular divideandconquer (DAC) applications at runtime and dynamic mapping to processors taking into account their speeds and even loads by other user processes. New implementations of parallel applications tuned for shortest execution time are investigated. They include £¥ ¤ search, recursive Fibonacci, ¦¨§©� � and finding twin prime numbers in parallel. Various DAC parameters were tuned for specific applications including costs of computing vectors/subtrees, maximum partitioning levels etc. Moreover, the overhead of DAMPVM/DAC compared to sequential implementations is shown including previously implemented adaptive quadrature integration and image recognition. 1
Transposition Table Driven Scheduling for TwoPlayer Games
, 2002
"... Gametree search is an important research topic in Artificial Intelligence. Because it is computationally intensive, researchers have turned their at tention to parallel gametree search algorithms in order to improve running time. However, achieving high parallel performance remains a difficult ta ..."
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Gametree search is an important research topic in Artificial Intelligence. Because it is computationally intensive, researchers have turned their at tention to parallel gametree search algorithms in order to improve running time. However, achieving high parallel performance remains a difficult task on distributedmemory systems. Many highperformance systems for two player games use the c/ search algorithm, enhanced with transposition tables. Transposition tables store useful information about gametrees from previous searches. When parallelizing the c algorithm, a major problem is sharing transposition table information efficiently among the processors. A processor must communicate in order to look up table entries on other processors, which hurts the performance of the parallel search.
Applying the Experience of Building a HighPerformance Search Engine for One Domain to Another
, 2002
"... This paper describes the highperformance alphabetabased search engine used in CHINOOK, the World ManMachine Checkers Champion. Previous experience in designing a chess program was important in the initial design of the program. As it evolved, however, numerous applicationspecific modifications ..."
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This paper describes the highperformance alphabetabased search engine used in CHINOOK, the World ManMachine Checkers Champion. Previous experience in designing a chess program was important in the initial design of the program. As it evolved, however, numerous applicationspecific modifications had to be made for the algorithms to excel at searching checkers trees. This paper describes the experience of transferring the technology used to develop a chess program to the creation of a highperformance checkers program.