On the Complexity of Connection Games
Bonnet, Edouard; Jamain, Florian; Saffidine, Abdallah (2016), On the Complexity of Connection Games, Theoretical Computer Science, 644, p. 2-28. 10.1016/j.tcs.2016.06.033
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01994450
Journal nameTheoretical Computer Science
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Abstract (EN)In this paper, we study three connection games among the most widely played: havannah, twixt, and slither. We show that determining the outcome of an arbitrary input position is PSPACE-complete in all three cases. Our reductions are based on the popular graph problem generalized geography and on hex itself. We also consider the complexity of generalizations of hex parameterized by the length of the solution and establish that while short generalized hex is W-hard, short hex is FPT. Finally, we prove that the ultra-weak solution to the empty starting position in hex cannot be fully adapted to any of these three games.
Subjects / KeywordsPSPACE; Slither; Hex; Complexity; Havannah; Twixt
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