Suboptimality of local algorithms for a class of max-cut problems

Wei Kuo Chen, David Gamarnik, Dmitry Panchenko, Mustazee Rahman

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


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 maxcut 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.

Original languageEnglish (US)
Pages (from-to)1587-1618
Number of pages32
JournalAnnals of Probability
Issue number3
StatePublished - May 1 2019

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2019.


  • Local algorithms
  • Maximum cut problems
  • Spin glasses


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