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On the Complexity of 2D Discrete Fixed Point Problem

(Extended Abstract)
  • Xi Chen
  • Xiaotie Deng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)

Abstract

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.

Keywords

Nash Equilibrium Directed Graph Turing Machine Point Problem Outgoing Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xi Chen
    • 1
  • Xiaotie Deng
    • 2
  1. 1.Department of Computer ScienceTsinghua University 
  2. 2.Department of Computer ScienceCity University of Hong Kong 

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