Multicut in Trees Viewed through the Eyes of Vertex Cover

We take a new look at the multicut problem in trees through the eyes of the vertex cover problem. This connection, together with other techniques that we develop, allows us to significantly improve the O(k) upper bound on the kernel size for multicut, given by Bousquet et al., to O(k). We exploit this connection further to present a parameterized algorithm for multicut that runs in time O∗(ρk), where ρ = ( √ 5 + 1)/2 ≈ 1.618. This improves the previous (time) upper bound of O∗(2k), given by Guo and Niedermeier, for the problem.