GAMES: A new Scenario for Software and Knowledge Reuse

Games are a well-known test bed for testing search algorithms and learning methods, and many authors have presented numerous reasons for the research in this area. Nevertheless, they have not received the attention they deserve as software projects. In this paper, we analyze the applicability of software and knowledge reuse in the games domain. In spite of the need to find a good evaluation function, search algorithms and interface design can be said to be the primary concerns. In addition, we will discuss the current state of the main statistical learning methods and how they can be addressed from a software engineering point of view. So, this paper proposes a reliable environment and adequate tools, necessary in order to achieve high levels of reuse in the games domain

Game tree algorithms and solution trees

In this paper, a theory of game tree algorithms is presented, entirely based upon the concept of solution tree. Two types of solution trees are distinguished: max and min trees. Every game tree algorithm tries to prune nodes as many as possible from the game tree. A cut-off criterion in terms of solution trees will be formulated, which can be used to eliminate nodes from the search without affecting the result. Further, we show that any algorithm actually constructs a superposition of a max and a min solution tree. Finally, we will see, how solution trees and the related cutoff criterion are applied in major game tree algorithms, like alpha-beta and MTD

Best-First and Depth-First Minimax Search in practice

Abstract Most practitioners use a variant of the Alpha-Beta algorithm, a simple depth-first procedure, for searching minimax trees. SSS*, with its best-first 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" best-first SSS* has cast doubt on the effectiveness of "dumb" depth-first Alpha-Beta

Trends in game tree search

This paper deals with algorithms searching trees generated by two-person, zero-sum games with perfect information. The standard algorithm in this field is alpha-beta. We will discuss this algorithm as well as extensions, like transposition tables, iterative deepening and NegaScout. Special attention is devoted to domain knowledge pertaining to game trees, more specifically to solution trees. The above mentioned algorithms implement depth first search. The alternative is best first search. The best known algorithm in this area is Stockman's SSS*. We treat a variant equivalent to SSS* called SSS-2. These algorithms are provably better than alpha-beta, but it needs a lot of tweaking to show this in practice. A variant of SSS-2, cast in alpha-beta terms, will be discussed which does realize this potential. This algorithm is however still worse than NegaScout. On the other hand, applying a similar idea as the one behind NegaScout to this last SSS version yields the best (sequential) game tree searcher known up till now: MTD(f)

A new paradigm for minimax search

This paper introduces a new paradigm for minimax game-tree search algorithms. MT is a memory-enhanced version of Pearl's Test procedure. By changing the way MT is called, a number of best-first game-tree search algorithms can be simply and elegantly constructed (including SSS*). Most of the assessments of minimax search algorithms have been based on simulations. However, these simulations generally do not address two of the key ingredients of high performance game-playing programs: iterative deepening and memory usage. This paper presents experimental data from three game-playing programs (checkers, Othello and chess), covering the range from low to high branching factor. The improved move ordering due to iterative deepening and memory usage results in significantly different results from those portrayed in the literature. Whereas some simulations show alpha-beta expanding almost 100% more leaf nodes than other algorithms [Marsland, Reinefeld & Schaeffer, 1987], our results showed variations of less than 20%. One new instance of our framework MTD(f) out-performs our best alpha-beta searcher (aspiration NegaScout) on leaf nodes, total nodes and execution time. To our knowledge, these are the first reported results that compare both depth-first and best-first algorithms given the same amount of memory

Searching informed game trees

Well-known algorithms for the evaluation of the minimax function in game trees are alpha-beta and SSS*. An improved version of SSS* is SSS-2. All these algorithms don't use any heuristic information on the game tree. In this paper the use of heuristic information is introduced into the alpha-beta and the SSS-2 algorithm. Extended versions of these algorithms are presented. The subset of nodes which is visited during execution of each algorithm is characterised completely

A theory of game trees, based on solution trees

In this paper a complete theory of game tree algorithms is presented, entirely based upon the notion of a solution tree. Two types of solution trees are distinguished: max and min solution trees respectively. We show that most game tree algorithms construct a superposition of a max and a min solution tree. Moreover, we formulate a general cut-off criterion in terms of solution trees. In the second half of this paper four well known algorithms, viz., alphabeta, SSS*, MTD and Scout are studied extensively. We show how solution trees feature in these algorithms and how the cut-off criterion is applied

The key node method: a highly-parallel alpha-beta algorithm

Journal ArticleA new parallel formulation of the alpha-beta algorithm for minimax game tree searching is presented. Its chief characteristic is incremental information sharing among subsearch processes in the form of "provisional" node value communication. Such "eager" communication can offer the double benefit of faster search focusing and enhanced parallelism. This effect is particularly advantageous in the prevalent case when static value correlation exists among adjacent nodes. A message-passing formulation of this idea, termed the "Key Node Method", is outlined. Preliminary experimental results for this method are reported, supporting its validity and potential for increased speedup