Almost 2-SAT Is Fixed-Parameter Tractable (Extended Abstract)

Authors:
Igor Razgon;Barry O'Sullivan
Affiliations:
Cork Constraint Computation Centre Computer Science Department, University College Cork, Ireland;Cork Constraint Computation Centre Computer Science Department, University College Cork, Ireland
Venue:
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Year:
2008

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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*m 3) time showing that this problem is fixed-parameter tractable.