Direction Preserving Zero Point Computing and Applications

Authors:
Xiaotie Deng;Qi Qi;Jie Zhang
Affiliations:
Department of Computer Science, City University of Hong Kong, Hong Kong SAR, P.R. China;Department of Management Science and Engineering, Stanford University, Stanford, USA;Department of Computer Science, City University of Hong Kong, Hong Kong SAR, P.R. China
Venue:
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Year:
2009

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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.