Algorithms For Cut Problems On Trees

We study the multicut on trees and the generalized multiway cut on trees problems. For the multicut on trees problem, we present a parameterized algorithm that runs in time O*(rho(k)), where rho = root root 2 + 1 approximate to 1.555 is the positive root of the polynomial x(4) - 2x(2) - 1. This improves the current- best algorithm of Chen et al. that runs in time O*( 1.619(k)). By reducing generalized multiway cut on trees to multicut on trees, our results give a parameterized algorithm that solves the generalized multiway cut on trees problem in time O*(rho(k)). We also show that the generalized multiway cut on trees problem is solvable in polynomial time if the number of terminal sets is a fixed constant.