A theoretical analysis of the k-satisfiability search space

Andrew M. Sutton; Adele E. Howe; L. Darrell Whitley

doi:10.1007/978-3-642-03751-1_4

A theoretical analysis of the k-satisfiability search space

Andrew M. Sutton, Adele E. Howe, L. Darrell Whitley

Computer Science (Duluth)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

8 Scopus citations

Abstract

Local search algorithms perform surprisingly well on the k-satisfiability (k-SAT) problem. However, few theoretical analyses of the k-SAT search space exist. In this paper we study the search space of the k-SAT problem and show that it can be analyzed by a decomposition. In particular, we prove that the objective function can be represented as a superposition of exactly k elementary landscapes. We show that this decomposition allows us to immediately compute the expectation of the objective function evaluated across neighboring points. We use this result to prove previously unknown bounds for local maxima and plateau width in the 3-SAT search space. We compute these bounds numerically for a number of instances and show that they are non-trivial across a large set of benchmarks.

Original language	English (US)
Title of host publication	Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings
Pages	46-60
Number of pages	15
DOIs	https://doi.org/10.1007/978-3-642-03751-1_4
State	Published - 2009
Event	2nd International Workshop on Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics, SLS 2009 - Brussels, Belgium Duration: Sep 3 2009 → Sep 4 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5752 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	2nd International Workshop on Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics, SLS 2009
Country/Territory	Belgium
City	Brussels
Period	9/3/09 → 9/4/09

Bibliographical note

Funding Information:
This research was sponsored by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number FA9550-08-1-0422. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.

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Sutton, A. M., Howe, A. E., & Whitley, L. D. (2009). A theoretical analysis of the k-satisfiability search space. In Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings (pp. 46-60). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5752 LNCS). https://doi.org/10.1007/978-3-642-03751-1_4

A theoretical analysis of the k-satisfiability search space. / Sutton, Andrew M.; Howe, Adele E.; Whitley, L. Darrell.
Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings. 2009. p. 46-60 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5752 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Sutton, AM, Howe, AE & Whitley, LD 2009, A theoretical analysis of the k-satisfiability search space. in Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5752 LNCS, pp. 46-60, 2nd International Workshop on Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics, SLS 2009, Brussels, Belgium, 9/3/09. https://doi.org/10.1007/978-3-642-03751-1_4

Sutton AM, Howe AE, Whitley LD. A theoretical analysis of the k-satisfiability search space. In Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings. 2009. p. 46-60. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-03751-1_4

Sutton, Andrew M. ; Howe, Adele E. ; Whitley, L. Darrell. / A theoretical analysis of the k-satisfiability search space. Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings. 2009. pp. 46-60 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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A theoretical analysis of the k-satisfiability search space

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