This article has three main contributions to our understanding of minimax search: First, a new formulation for Stockman's SSS* algorithm, based on Alpha-Beta, is presented. It solves all the perceived drawbacks of SSS*, finally transforming it into a practical algorithm. In effect, we show that SSS* = Alpha-Beta + transposition tables. The crucial step is the realization that transposition tables contain so-called solution trees, structures that are used in best-first search algorithms like SSS*. Having created a practical version, we present performance measurements with tournament game-playing programs for three different mini-max games, yielding results that contradict a number of publications. Second, based on the insights gained in our attempts at understanding SSS*, we present a framework that facilitates the construction of several best-first fixed-depth game-tree search algorithms, known and new. The framework is based on depth-first null-window Alpha-Beta search, enhanced with storage to allow for the refining of previous search results. It focuses attention on the essential differences between algorithms. Third, a new instance of this framework is presented. It performs better than algorithms that are currently used in most state-of-the-art game-playing programs. We provide experimental evidence to explain why this new algorithm, MTD(ƒ), performs better than other fixed-depth minimax algorithms.
Distributed simulation, more specifically the HLA standard, is hardly applied in industry. We have conducted an extensive survey with COTS (commercial off-the-shelf) simulation package vendors and simulation experts, both from defence and industry, that focuses, amongst others, on the question what the reasons are behind this phenomenon. In this paper we analyze the reactions that we obtained, categorizing them into arguments related to distributed simulation in general, arguments related to HLA and arguments pertaining to the embedding of HLA concepts in COTS packages. These answers will lead us, we believe, to insights that can serve as guidelines to make distributed simulation more attractive for the industrial simulation community.
This article has three main contributions to our understanding of minimax search:First, 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* = Alpha-Beta + transposition tables. The crucial step is the realization that transposition tables contain so-called solution trees, structures that are used in best-first search algorithms like SSS*. Having created a practical version, we present performance measurements with tournament game-playing programs for three different minimax games, yielding results that contradict a number of publications.Second, based on the insights gained in our attempts at understanding SSS*, we present a framework that facilitates the construction of several best-first fixeddepth game-tree search algorithms, known and new. The framework is based on depth-first null-window Alpha-Beta search, enhanced with storage to allow for the refining of previous search results. It focuses attention on the essential differences between algorithms.Third, a new instance of this framework is presented. It performs better than algorithms that are currently used in most state-of-the-art game-playing programs. We provide experimental evidence to explain why this new algorithm, MTD(ƒ), performs better than other fixed-depth minimax algorithms.
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