Approximating CSPs using LP relaxation

Subhash Khot, Rishi Saket

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper studies how well the standard LP relaxation approximates a k-ary constraint satisfaction problem (CSP) on label set [L]. We show that, assuming the Unique Games Conjecture, it achieves an approximation within O(k3 ・ log L) of the optimal approximation factor. In particular we prove the following hardness result: let I be a k-ary CSP on label set [L] with constraints from a constraint class C, such that it is a (c, s)-integrality gap for the standard LP relaxation. Then, given an instance H with constraints from C, it is NP-hard to decide whether, (Formula Presented.) assuming the Unique Games Conjecture. We also show the existence of an efficient LP rounding algorithm Round such that given an instance H from a permutation invariant constraint class C which is a (c, s)-rounding gap for Round, it is NP-hard to decide whether, (Formula Presented.) assuming the Unique Games Conjecture.

Original languageEnglish (US)
Title of host publicationAutomata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings
EditorsMagnus M. Halldorsson, Naoki Kobayashi, Bettina Speckmann, Kazuo Iwama
PublisherSpringer Verlag
Pages822-833
Number of pages12
ISBN (Print)9783662476710
DOIs
StatePublished - Jan 1 2015
Event42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 - Kyoto, Japan
Duration: Jul 6 2015Jul 10 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9134
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other42nd International Colloquium on Automata, Languages and Programming, ICALP 2015
CountryJapan
CityKyoto
Period7/6/157/10/15

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Khot, S., & Saket, R. (2015). Approximating CSPs using LP relaxation. In M. M. Halldorsson, N. Kobayashi, B. Speckmann, & K. Iwama (Eds.), Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings (pp. 822-833). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9134). Springer Verlag. https://doi.org/10.1007/978-3-662-47672-7_67