Abstract
We introduce a distinction, in single-agent problems, between transpositions that are due to permutations of commutative moves and transpositions that are not. We show a simple modification of a depth-first search algorithm which can detect the transpositions of the first class without the use of a transposition table. It works by maintaining, for each node, a list of moves that are known to lead to transpositions. This algorithm is applied to two one-player games: a solitary card game called Gaps, and a game called Morpion Solitaire. We analyze, for each domain, how often transpositions are due to commutative moves. In one variant of Gaps, the algorithm enables to search more efficiently with a small transposition table. In Morpion Solitaire, a transposition table is not even needed. The best known sequence for this game is proved optimal for more than one hundred moves.
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References
Breuker, D.M.: Memory versus Search in Games. PhD thesis, Maastricht University (1998)
Helmstetter, B., Cazenave, T.: Searching with analysis of dependencies in a solitaire card game. In: van den Herik, H.J., Iida, H., Heinz, E.A. (eds.) Advances in Computer Games 10: Many Games, Many Challenges, pp. 343–360. Kluwer, Dordrecht (2003)
Juillé, H.: Incremental co-evolution of organisms: A new approach for optimization and discovery of strategies. In: Morán, F., Merelo, J.J., Moreno, A., Chacon, P. (eds.) ECAL 1995. LNCS, vol. 929, pp. 246–260. Springer, Heidelberg (1995)
Juillé, H.: Methods for Statistical Inference: Extending the Evolutionary Computation Paradigm. PhD thesis, Brandeis University (1999)
Meyrignac, J.-C.: Morpion solitaire progress, http://euler.free.fr/morpion.htm
Shintani, T.: Consideration about state transition in Superpuzz. In: Information Processing Society of Japan Meeting, Shonan, Japan, pp. 41–48 (2000) (In Japanese)
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© 2006 Springer-Verlag Berlin Heidelberg
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Helmstetter, B., Cazenave, T. (2006). Incremental Transpositions. In: van den Herik, H.J., Björnsson, Y., Netanyahu, N.S. (eds) Computers and Games. CG 2004. Lecture Notes in Computer Science, vol 3846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11674399_15
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DOI: https://doi.org/10.1007/11674399_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32488-1
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