  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.
