SUBOPTIMALITY OF LOCAL ALGORITHMS FOR A CLASS OF MAX-CUT PROBLEMS

• 成果类型: Article
• 署名作者: Chen, Wei-Kuo; Gamarnik, David; Panchenko, Dmitry; Rahman, Mustazee
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of Toronto; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1291
• 发表日期: 2019
• 页码: 1587-1618
• 关键词: parisi formula; spin; bounds; LIMITS; FIELDS

摘要

We show that in random K-uniform hypergraphs of constant average degree, for even K >= 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.