Almost 2-SAT is Fixed-Parameter Tractable
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', '2-SAT deletion'. The status of 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 which solves this problem in O(15k*k*m3) and thus we show that this problem is fixed-parameter tractable.
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