In this paper we consider two above lower bound parameterizations of the Node Multiway Cut problem - above the 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 an O*(2^k) algorithm for Node Multiway Cut with a standard parameterization by the solution size, improving previous bounds for these problems.
@article{arxiv.1107.1585,
title = {On Multiway Cut parameterized above lower bounds},
author = {Marek Cygan and Marcin Pilipczuk and Michał Pilipczuk and Jakub Onufry Wojtaszczyk},
journal= {arXiv preprint arXiv:1107.1585},
year = {2011}
}