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May 2019 Suboptimality of local algorithms for a class of max-cut problems
Wei-Kuo Chen, David Gamarnik, Dmitry Panchenko, Mustazee Rahman
Ann. Probab. 47(3): 1587-1618 (May 2019). DOI: 10.1214/18-AOP1291

Abstract

We show that in random $K$-uniform hypergraphs of constant average degree, for even $K\geq 4$, local algorithms defined as factors of i.i.d. can not find nearly maximal cuts, when the average degree is sufficiently large. These algorithms have been used frequently to obtain lower bounds for the max-cut problem on random graphs, but it was not known whether they could be successful in finding nearly maximal cuts. This result follows from the fact that the overlap of any two nearly maximal cuts in such hypergraphs does not take values in a certain nontrivial interval—a phenomenon referred to as the overlap gap property—which is proved by comparing diluted models with large average degree with appropriate fully connected spin glass models and showing the overlap gap property in the latter setting.

Citation

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Wei-Kuo Chen. David Gamarnik. Dmitry Panchenko. Mustazee Rahman. "Suboptimality of local algorithms for a class of max-cut problems." Ann. Probab. 47 (3) 1587 - 1618, May 2019. https://doi.org/10.1214/18-AOP1291

Information

Received: 1 July 2017; Revised: 1 March 2018; Published: May 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07067277
MathSciNet: MR3945754
Digital Object Identifier: 10.1214/18-AOP1291

Subjects:
Primary: 60K35
Secondary: 05C80, 60F10, 60G15, 68W20, 82B44

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 3 • May 2019
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