On the Complexity of Connection Games

Bonnet, Edouard; Jamain, Florian; Saffidine, Abdallah

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

Type

Article accepté pour publication ou publié

External document link

https://hal.archives-ouvertes.fr/hal-01994450

Date

2016

Journal name

Theoretical Computer Science

Volume

644

Publisher

Elsevier

Pages

2-28

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[1]-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 / Keywords

PSPACE; Slither; Hex; Complexity; Havannah; Twixt