NC algorithms for computing the number of perfect matchings in K3,3-free graph and related problems
Information and Computation
On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Parallel Algorithms for $K_{5}$-minor Free Graphs
Parallel Algorithms for $K_{5}$-minor Free Graphs
On the Complexity of Two-PlayerWin-Lose Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Efficient computation of nash equilibria for very sparse win-lose bimatrix games
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
The approximation complexity of win-lose games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
Planar Graph Isomorphism is in Log-Space
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
The Complexity of Computing a Nash Equilibrium
SIAM Journal on Computing
Reachability In K3,3-free graphs and K5-free graphs is in unambiguous log-space
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
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Finding a Nash equilibrium in a bimatrix game is PPAD-hard (Chen and Deng, 2006 [5], Chen, Deng and Teng, 2009 [6]). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and Valiant, 2005 [1]). However, there do exist polynomial time tractable classes of win-lose bimatrix games - such as, very sparse games (Codenotti, Leoncini and Resta, 2006 [8]) and planar games (Addario-Berry, Olver and Vetta, 2007 [2]). We extend the results in the latter work to K3,3 minor-free games and a subclass of K5 minor-free games. Both these classes strictly contain planar games. Further, we sharpen the upper bound to unambiguous logspace UL, a small complexity class contained well within polynomial time P. Apart from these classes of games, our results also extend to a class of games that contain both K3,3 and K5 as minors, thereby covering a large and non-trivial class of win-lose bimatrix games. For this class, we prove an upper bound of nondeterministic logspace NL, again a small complexity class in P. Our techniques are primarily graph theoretic and use structural characterizations of the considered minor-closed families.