Approximation of non-boolean 2CSP

Guy Kindler, Alexandra Rolla, Luca Trevisan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

We develop a polynomial time ω(1/R log R) approximate algorithm for Max 2CSP-.R, the problem where we are given a collection of constraints, each involving two variables, where each variable ranges over a set of size R, and we want to find an assignment to the variables that maximizes the number of satisfied constraints. Assuming the Unique Games Conjecture, this is the best possible approximation up to constant factors. Previously, a 1/R-approximate algorithm was known, based on linear programming. Our algorithm is based on semidefinite programming. The Semidefinite Program that we use has an almost-matching integrality gap. For the more general Max kCSP-R, in which each constraint involves k variables, each ranging over a set of size R, it was known that the best possible approximation is of the order of k/Rk-1, provided that k is sufficiently large compared to R; our algorithm shows that the bound k/Rk-1 is not tight for k = 2.

Original languageAmerican English
Title of host publication27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
EditorsRobert Krauthgamer
PublisherAssociation for Computing Machinery
Pages1705-1714
Number of pages10
ISBN (Electronic)9781510819672
StatePublished - 2016
Event27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 - Arlington, United States
Duration: 10 Jan 201612 Jan 2016

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume3

Conference

Conference27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
Country/TerritoryUnited States
CityArlington
Period10/01/1612/01/16

Bibliographical note

Publisher Copyright:
© (2016) by SIAM: Society for Industrial and Applied Mathematics.

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