1996
DOI: 10.1016/0004-3702(95)00126-3
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Best-first fixed-depth minimax algorithms

Abstract: 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 create… Show more

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Cited by 86 publications
(32 citation statements)
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“…This is a minimax problem, which we solve by extending the approach from [5], called optimistic minimax search (OMS). OMS explores a tree representation of the possible sequences of max and min agent actions (here, mode switches); it is a variant of B* [17] and related to other classical minimax search methods [10], [18], [12]. It returns a near-optimal sequence with respect to the minimax-optimal value.…”
Section: Introductionmentioning
confidence: 99%
“…This is a minimax problem, which we solve by extending the approach from [5], called optimistic minimax search (OMS). OMS explores a tree representation of the possible sequences of max and min agent actions (here, mode switches); it is a variant of B* [17] and related to other classical minimax search methods [10], [18], [12]. It returns a near-optimal sequence with respect to the minimax-optimal value.…”
Section: Introductionmentioning
confidence: 99%
“…• It is possible, but unimplemented, to further reduce the search space for split by observing that our dynamic programming solution has the same structure as a minimax problem allowing us to exploit alpha-beta pruning [9], computing an alpha-beta bounded transposition table rather than a classic dynamic program. MTD(f) [18] is a particularly applicable pruning technique, because the length of a do expression acts as a conservative upper bound on our cost function, our result is an integer drawn from a very small range, and our transposition table is considerably smaller than that of most games to which it has been applied. MTD(f) would not improve the worst-case cost of computing an optimal solution, but based on limited experimentation, it should bring some extreme examples, such as the one in Section 5.4, back into line with heuristic compile times.…”
Section: Discussionmentioning
confidence: 99%
“…However, since it is a BFS, search consumes a large amount of memory and therefore for problems with large sizes, its performance can often be unsatisfactory. In addition, it is difficult to demonstrate the correctness of intuitively, as pointed out by [24]. For the above problems, Plaat et al [21]- [24] proposed the MTD(f) algorithm in a BFS version, or alternatively in a depth-first search (DFS) version with the help of transposition tables to improve efficiency.…”
Section: The Family Of Alpha-beta Searchmentioning
confidence: 98%
“…In addition, it is difficult to demonstrate the correctness of intuitively, as pointed out by [24]. For the above problems, Plaat et al [21]- [24] proposed the MTD(f) algorithm in a BFS version, or alternatively in a depth-first search (DFS) version with the help of transposition tables to improve efficiency. It obtains the benefit of expanding fewer nodes in experiments while consuming significantly less memory.…”
Section: The Family Of Alpha-beta Searchmentioning
confidence: 98%
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