Suboptimality of local algorithms for a class of max-cut problems
Name
1707.05386.pdf
Description
Submitted version
Size
285.96 KB
Format
Adobe PDF
Checksum (MD5)
cb93cc700413a90b3f62d70ef28274b4
Author(s)
Chen, Wei-Kuo
Gamarnik, David
Panchenko, Dmitry
Rahman, Mustazee
Date Issued
2019
Journal
The Annals of Probability
Publisher
Institute of Mathematical Statistics
Version
Original manuscript
Abstract
© Institute of Mathematical Statistics, 2019. 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.
MIT Department
Sloan School of Management
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/18-AOP1291
