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.
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
14 October 2011
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), .
(doi:10.1287/moor.1110.0511).
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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Published date: 14 October 2011
Organisations:
Agents, Interactions & Complexity
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Local EPrints ID: 402590
URI: http://eprints.soton.ac.uk/id/eprint/402590
ISSN: 0364-765X
PURE UUID: f50d0f26-3f12-40ef-9772-232a54a2d376
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Date deposited: 29 Nov 2016 16:34
Last modified: 15 Mar 2024 03:22
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Author:
Xiaotie Deng
Author:
Qi Qi
Author:
Amin Saberi
Author:
Jie Zhang
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