Almost 2-SAT is fixed-parameter tractable

Igor Razgon; Barry O'Sullivan

doi:10.1016/j.jcss.2009.04.002

Almost 2-SAT is fixed-parameter tractable

Igor Razgon, Barry O'Sullivan

Research output: Contribution to journal › Article › peer-review

110 Scopus citations

Abstract

We consider the following problem. Given a 2-cnf formula, is it possible to remove at most k clauses so that the resulting 2-cnf formula is satisfiable? This problem is known to different research communities in theoretical computer science under the names Almost 2-SAT, All-but-k 2-SAT, 2-cnf deletion, and 2-SAT deletion. The status of the fixed-parameter tractability of this problem is a long-standing open question in the area of parameterized complexity. We resolve this open question by proposing an algorithm that solves this problem in O (15^k × k × m³) time showing that this problem is fixed-parameter tractable.

Original language	English
Pages (from-to)	435-450
Number of pages	16
Journal	Journal of Computer and System Sciences
Volume	75
Issue number	8
DOIs	https://doi.org/10.1016/j.jcss.2009.04.002
State	Published - 1 Jan 2009
Externally published	Yes

Keywords

Fixed-parameter algorithms
Satisfiability problems
Separation problems

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1016/j.jcss.2009.04.002

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AU - O'Sullivan, Barry

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AB - We consider the following problem. Given a 2-cnf formula, is it possible to remove at most k clauses so that the resulting 2-cnf formula is satisfiable? This problem is known to different research communities in theoretical computer science under the names Almost 2-SAT, All-but-k 2-SAT, 2-cnf deletion, and 2-SAT deletion. The status of the fixed-parameter tractability of this problem is a long-standing open question in the area of parameterized complexity. We resolve this open question by proposing an algorithm that solves this problem in O (15k × k × m3) time showing that this problem is fixed-parameter tractable.

KW - Fixed-parameter algorithms

KW - Satisfiability problems

KW - Separation problems

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EP - 450

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

IS - 8

ER -

Almost 2-SAT is fixed-parameter tractable

Abstract

Keywords

ASJC Scopus subject areas

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