2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159011We 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 $O(15^k*k*m^3)$ and thus we show that this problem is fixed-parameter tractable.This new version fixes the bug found by Somnath Sikdar in the proof of Claim 8. In the repaired version the modification of the Almost 2-SAT problem called 2-SLASAT is no longer needed and only the modification called 2-ASLASAT remains relevant. Hence the whole manuscript is updated so that the 2-SLASAT problem is not mentioned there anymoreData Structures and AlgorithmsComputational GeometryLogic in Computer Sciencetext