On multiway cut parameterized above lower bounds

Authors:
Marek Cygan;Marcin Pilipczuk;Michał Pilipczuk;Jakub Onufry Wojtaszczyk
Affiliations:
University of Warsaw, Poland;University of Warsaw, Poland;University of Warsaw, Poland;Google Inc., Warsaw, Poland
Venue:
ACM Transactions on Computation Theory (TOCT)
Year:
2013

Citing 18
Cited 2

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Abstract

We introduce a concept of parameterizing a problem above the optimum solution of its natural linear programming relaxation and prove that the node multiway cut problem is fixed-parameter tractable (FPT) in this setting. As a consequence we prove that node multiway cut is FPT, when parameterized above the maximum separating cut, resolving an open problem of Razgon. Our results imply O*(4k) algorithms for vertex cover above maximum matching and almost 2-SAT as well as an O*(2k) algorithm for node multiway cut with a standard parameterization by the solution size, improving previous bounds for these problems.