Experiments With Some Programs That Search Game Trees
Journal of the ACM (JACM)
A game theory approach to high-level strategic planning in first person shooters
IE '08 Proceedings of the 5th Australasian Conference on Interactive Entertainment
Semantic comparison of structured visual dataflow programs
Proceedings of the 3rd International Symposium on Visual Information Communication
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An analysis of the alpha-beta pruning algorithm is presented which takes into account both shallow and deep cut-offs. A formula is first developed to measure the average number of terminal nodes examined by the algorithm in a uniform free of degree n and depth d when ties are allowed among the bottom positions: specifically, all bottom values are assumed to be independent identically distributed random variables drawn from a discrete probability distribution. A worst case analysis over all possible probability distributions is then presented by considering the limiting case when the discrete probability distribution tends to a continuous probability distribution. The branching factor of the alpha-beta pruning algorithm is shown to grow with n as &THgr;(n/In n), therefore confirming a claim by Knuth and Moore that deep cut-offs only have a second order effect on the behavior of the algorithm.