The normalized autocorrelation length of random max r-Sat converges in probability to (1 − 1/2r)/r

Daniel Berend, Yochai Twitto

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

2 Scopus citations

Abstract

In this paper we show that the so-called normalized auto- correlation length of random Max r-Sat converges in probability to (1 − 1/2r)/r, where r is the number of literals in a clause. We also show that the correlation between the numbers of clauses satisfied by a random pair of assignments of distance d = cn, 0 ≤ c ≤ 1, converges in probability to ((1 − c)r − 1/2r)/(1 − 1/2r). The former quantity is of interest in the area of landscape analysis as a way to better understand problems and assess their hardness for local search heuristics. In [34], it has been shown that it may be calculated in polynomial time for any instance, and its mean value over all instances was discussed. Our results are based on a study of the variance of the number of clauses satisfied by a random assignment, and the covariance of the numbers of clauses satisfied by a random pair of assignments of an arbitrary distance. As part of this study, closed-form formulas for the expected value and vari- ance of the latter two quantities are provided. Note that all results are relevant to random r-Sat as well.

Original languageEnglish
Title of host publicationTheory and Applications of Satisfiability Testing – SAT 2016 - 19th International Conference, Proceedings
EditorsDaniel Le Berre, Nadia Creignou
PublisherSpringer Verlag
Pages60-76
Number of pages17
ISBN (Print)9783319409696
DOIs
StatePublished - 1 Jan 2016
Event19th International Conference on Theory and Applications of Satisfiability Testing, SAT 2016 - Bordeaux, France
Duration: 5 Jul 20168 Jul 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9710
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th International Conference on Theory and Applications of Satisfiability Testing, SAT 2016
Country/TerritoryFrance
CityBordeaux
Period5/07/168/07/16

Keywords

  • Autocorrelation length
  • Combinatorial
  • Fitness landscapes
  • Local search
  • Max sat
  • Optimization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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