Almost 2-SAT is fixed-parameter tractable

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 de...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 75; no. 8; pp. 435 - 450
Main Authors: Razgon, Igor, O'Sullivan, Barry
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2009
Subjects:
Fixed-parameter algorithms
Satisfiability problems
Separation problems
Separation problems
Fixed-parameter algorithms
Satisfiability problems
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary: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 × m 3 ) time showing that this problem is fixed-parameter tractable.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2009.04.002