WINE 2009: Internet and Network Economics pp 410-421 | Cite as

Direction Preserving Zero Point Computing and Applications

(Extended Abstract)
  • Xiaotie Deng
  • Qi Qi
  • Jie Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5929)

Abstract

We study the connection between the direction preserving zero point and the discrete Brouwer fixed point in terms of their computational complexity. As a result, we derive a PPAD-completeness proof for finding a direction preserving zero point, and a matching oracle complexity bound for computing a discrete Brouwer’s fixed point.

Building upon the connection between the two types of combinatorial structures for Brouwer’s continuous fixed point theorem, we derive an immediate proof that TUCKER is PPAD-complete for all constant dimensions, extending the results of Pálvölgyi for 2D case [20] and Papadimitriou for 3D case [21]. In addition, we obtain a matching algorithmic bound for TUCKER in the oracle model.

Keywords

Nash Equilibrium Polynomial Time Algorithm Constant Dimension Fair Division Unit Hypercube 
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 2009

Authors and Affiliations

  • Xiaotie Deng
    • 1
  • Qi Qi
    • 2
  • Jie Zhang
    • 1
  1. 1.Department of Computer ScienceCity University of Hong KongHong Kong SARP.R. China
  2. 2.Department of Management Science and EngineeringStanford UniversityStanfordUSA

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