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Discrete fixed points: models, complexities, and applications

Discrete fixed points: models, complexities, and applications
Discrete fixed points: models, complexities, and applications
We study three discrete fixed point concept (SPERNER, DPZP, BROUWER) under two different models: the polynomial-time function model and the oracle function model. We fully characterize the computational complexities of these three problems. The computational complexity unification of the above problems gives us more choices in the study of different applications. As an example, by a reduction from DPZP, we derive asymptotically equal lower and upper bound for TUCKER in the oracle model. The same reduction also allows us to derive a single proof for the PPAD-completeness of TUCKER in any constant dimension, which is significantly simpler than the recent proofs.
0364-765X
636-652
Deng, Xiaotie
772c0705-a735-43dc-8988-f5c527572574
Qi, Qi
52d10c75-5466-4e04-9e85-5b4773dfbb56
Saberi, Amin
ba8cdf99-c2e2-4d7f-8889-bbe90047ca47
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a
Deng, Xiaotie
772c0705-a735-43dc-8988-f5c527572574
Qi, Qi
52d10c75-5466-4e04-9e85-5b4773dfbb56
Saberi, Amin
ba8cdf99-c2e2-4d7f-8889-bbe90047ca47
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a

Deng, Xiaotie, Qi, Qi, Saberi, Amin and Zhang, Jie (2011) Discrete fixed points: models, complexities, and applications. Mathematics of Operations Research, 36 (4), 636-652. (doi:10.1287/moor.1110.0511).

Record type: Article

Abstract

We study three discrete fixed point concept (SPERNER, DPZP, BROUWER) under two different models: the polynomial-time function model and the oracle function model. We fully characterize the computational complexities of these three problems. The computational complexity unification of the above problems gives us more choices in the study of different applications. As an example, by a reduction from DPZP, we derive asymptotically equal lower and upper bound for TUCKER in the oracle model. The same reduction also allows us to derive a single proof for the PPAD-completeness of TUCKER in any constant dimension, which is significantly simpler than the recent proofs.

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More information

Published date: 14 October 2011
Organisations: Agents, Interactions & Complexity

Identifiers

Local EPrints ID: 402590
URI: https://eprints.soton.ac.uk/id/eprint/402590
ISSN: 0364-765X
PURE UUID: f50d0f26-3f12-40ef-9772-232a54a2d376
ORCID for Jie Zhang: ORCID iD orcid.org/0000-0003-1380-9952

Catalogue record

Date deposited: 29 Nov 2016 16:34
Last modified: 06 Jun 2018 12:14

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Contributors

Author: Xiaotie Deng
Author: Qi Qi
Author: Amin Saberi
Author: Jie Zhang ORCID iD

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