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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Vydáno v:Journal of computer and system sciences Ročník 75; číslo 8; s. 435 - 450
Hlavní autoři: Razgon, Igor, O'Sullivan, Barry
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.12.2009
Témata:
Fixed-parameter algorithms
Satisfiability problems
Separation problems
Separation problems
Fixed-parameter algorithms
Satisfiability problems
ISSN:0022-0000, 1090-2724
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Shrnutí: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