On the Complexity of 2D Discrete Fixed Point Problem
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  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 . 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.
KeywordsNash Equilibrium Directed Graph Turing Machine Point Problem Outgoing Edge
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