The paper investigates the efficiency of parallel minimax algorithms for search in a game tree. The game used as a case study is a tic-tac-toe. The suggested parallel computational model exploits tree partitioning at width for each level of the game tree and is based on combination of the parallel algorithmic paradigms "manager-workers" and "asynchronous iterations". Performance comparison has been made for hybrid (multilevel,) flat and multithreaded parallel programming models. Speedup and efficiency as well as scalability in respect to the size of the multicomputer and its impact on the performance of the parallel system have been estimated on the basis of experimental results. The communication/computation ratio (CCR) of the parallel hybrid and flat implementations of the minimax algorithm has been estimated. INTRODUCTIONSearch algorithms are essential part of algorithms for solving many problems in computer science with a lot of practical applications such as database systems, expert systems, robot control systems, theorem-provers. Game-playing systems have search engines at the core of the application. A number of search algorithms have been proposed to improve the search efficiency in many practical applications such as branch and bound, minimax algorithm, alpha-beta pruning, etc.[1].A game tree in the game theory is defined as a tree with vertices denoting different game layouts and edges being the possible moves from one position to another. Tree searching is fundamental and computationally intensive problem. Minimax algorithm is a combinatorial optimization algorithm for search in a game tree.A sequential game tree search algorithm uses single processor to search the game tree. In order to be able to search at greater search depths in reasonable time multiple processors can be utilized for parallel computing [2,3].Clusters of the shared-memory architectural style have become popular nowadays as well as hyperthreading and multicore processors. Consequently, shared memory parallel programming models are emerging as a serious competitive environment to message passing. Hybrid (multi-level) parallel programming model is based on a combination of the two approaches -high-level parallelism afforded by message-passing and low-level parallelism used for loop level multithreaded parallelism.In this paper the efficiency of parallel minimax algorithm for game tree search on multicomputer platform is investigated. The game used as a case study is a tic-tac-toe. The suggested parallel computational model is based on parallel programming paradigm "manager-worker". Hybrid (multilevel) programming model is employed and compared to the performance parameters obtained by message passing and multithreading parallel programming models. Speedup and efficiency are explored on the basis of experimental results obtained. Analysis of the experimental results and parallel performance profiling are aimed at investigation of the algorithm scalability in respect to the size of the multicomputer.

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