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Direction preserving zero point computing and applications

Direction preserving zero point computing and applications
Direction preserving zero point computing and applications
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.
410-421
Deng, Xiaotie
772c0705-a735-43dc-8988-f5c527572574
Qi, Qi
52d10c75-5466-4e04-9e85-5b4773dfbb56
Zhang, Jie
21de2303-4727-4097-9b0f-ae43d95d052a
Deng, Xiaotie
772c0705-a735-43dc-8988-f5c527572574
Qi, Qi
52d10c75-5466-4e04-9e85-5b4773dfbb56
Zhang, Jie
21de2303-4727-4097-9b0f-ae43d95d052a

Deng, Xiaotie, Qi, Qi and Zhang, Jie (2009) Direction preserving zero point computing and applications. pp. 410-421 . (doi:10.1007/978-3-642-10841-9_37).

Record type: Conference or Workshop Item (Other)

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.

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Published date: 2009
Organisations: Agents, Interactions & Complexity

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Local EPrints ID: 402594
URI: http://eprints.soton.ac.uk/id/eprint/402594
PURE UUID: edfc6765-7e0d-4df7-97ae-c6ce92eace12

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Date deposited: 29 Nov 2016 16:39
Last modified: 15 Jul 2019 19:55

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