... This paper draws upon experiences gained during the development of programs which search chess game trees. Over the past decade major enhancements to the alpha-beta algorithm have been developed by people building game-playing programs, and many of these methods will be surveyed and compared here. The balance of the paper contains a study of contemporary methods for searching chess game trees in parallel, using an arbitrary number of independent processors. To make efficient use of these processors, one must have a clear understanding of the basic properties of the trees actually traversed when alpha-beta cutoffs occur. This paper provides such insights and concludes with a brief description of our own refinement to a standard parallel search algorithm for this problem.

Since the beginning of AI, mind games have been studied as relevant application fields. Nowadays, some programs are better than human players in most classical games. Their results highlight the efficiency of AI methods that are now quite standard. Such methods are very useful to Go programs, but they do not enable a strong Go program to be built. The problems related to Computer Go require new AI problem solving methods. Given the great number of problems and the diversity of possible solutions, Computer Go is an attractive research domain for AI. Prospective methods of programming the game of Go will probably be of interest in other domains as well. The goal of this paper is to present Computer Go by showing the links between existing studies on Computer Go and different AI related domains: evaluation function, heuristic search, machine learning, automatic knowledge generation, mathematical morphology and cognitive science. In addition, this paper describes both the practical aspects of Go programming, such as program optimization, and various theoretical aspects such as combinatorial game theory, mathematical morphology, and MonteCarlo methods. B. Bouzy T. Cazenave page 2 08/06/01 1.

Iterative-deepening searches mimic a breadth-first node expansion with a series of depth-first searches that operate with successively extended search horizons. They have been proposed as a simple way to reduce the space complexity of best-first searches like A* from exponential to linear in the search depth.

We introduce a new technique for constructing a family of universal hash functions.

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There is a well-known class of message authentication systems guaranteeing that attackers will have a negligible chance of successfully forging a message. This paper shows how one of these systems can hash messages at extremely high speed -- much more quickly than previous systems at the same security level -- using IEEE floating-point arithmetic. This paper also presents a survey of the literature in a unified mathematical framework.

Most parallel game-tree search approaches use synchronous methods, where the work is concentrated within a specific part of the tree, or at a given search depth. This article shows that asynchronous game-tree search algorithms can be as efficient as or better than synchronous methods in determining the minimax value. APHID, a new asynchronous parallel game-tree search algorithm, is presented. APHID is implemented as a freely-available portable library, making the algorithm easy to integrate into a sequential game-tree searching program. APHID has been added to four programs written by different authors. APHID yields better speedups than synchronous search methods for an Othello and a checkers program, and comparable speedups on two chess programs.

The 8-puzzle is the largest puzzle of its type that can be completely solved. It is simple, and yet obeys a combinatorially large problem space of 9!/2 states. The N x N extension of the 8-puzzle is NP-hard. In the first part of this paper, we present complete statistical data based on an exhaustive evaluation of all possible tile configurations. Our results include data on the expected solution lengths, the `easiest ' and `worst' configurations, and the density and distribution of solution nodes in the search tree. In our second set of experiments, we used the 8-puzzle as a workbench model to evaluate the benefit of node ordering schemes in Iterative-Deepening A* (IDA*. One highlight of our results is that almost all IDA* implementations perform worse than would be possible with a simple random ordering of the operators.

This paper discusses a new work-scheduling algorithm for parallel search of single-agent state spaces, called 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 128-processor parallel machine show that the scheme achieves close-to-linear 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 work-stealing-based schemes.

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