Fixed-parameter tractability of multicut parameterized by the size of the cutset

Abstract

Given an undirected graph $G$, a collection $\{(s_1,t_1),...,(s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every $s_i$ from the corresponding $t_i$. Vertex Multicut is the analogous problem where $S$ is a set of at most $p$ vertices. Our main result is that both problems can be solved in time $2^{O(p^3)}...n^{O(1)}$, i.e., fixed-parameter tractable parameterized by the size $p$ of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form $f(p)...n^{O(1)}$ exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset.

References in corpus (1)

• A Polynomial Kernel For Multicut In Trees

Cited by in corpus (4)

• List H-Coloring a Graph by Removing Few Vertices
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• On Polynomial Kernels for Structural Parameterizations of Odd Cycle Transversal