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On Multiway Cut paramterized above lower bounds

Marek Cygan
Marcin Pilipczuk
Michał Pilipczuk
IPEC 2011 (to appear)


In this paper we consider two above lower bound parameterizations of Node Multiway Cut — above maximum separating cut and above a natural LP-relaxation — and prove them to be fixed-parameter tractable. Our results imply O(4^k) algorithms for Vertex Cover above Maximum Matching and Almost 2-SAT as well as a O*(2^k) algorithm for Node Multiway Cut with a standard parameterization by the solution size, improving previous bounds for these problems.