Exponential lower bounds for finding Brouwer fixed points
Journal of Complexity
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
A sperner lemma complete for PPA
Information Processing Letters
On algorithms for discrete and approximate brouwer fixed points
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On graph-theoretic lemmata and complexity classes
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
The NP-completeness column: Finding needles in haystacks
ACM Transactions on Algorithms (TALG)
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
Direction Preserving Zero Point Computing and Applications
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
A direct reduction from k-player to 2-player approximate nash equilibrium
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
A simplicial approach for discrete fixed point theorems
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
| Hi-index | 0.00 |
While the 3-dimensional analogue of Sperner's problem in the plane was known to be complete in class PPAD, the complexity of 2D-SPERNER itself is not known to be PPAD-complete or not. In this paper, we settle this open problem proposed by Papadimitriou [9] fifteen years ago. The result also allows us to derive the computational complexity characterization of a discrete version of the 2-dimensional Brouwer fixed point problem, improving a recent result of Daskalakis, Goldberg and Papadimitriou [4]. Those hardness results for the simplest version of those problems provide very useful tools to the study of other important problems in the PPAD class.