A simple algorithm for multicuts in planar graphs with outer terminals

Abstract

Given an edge-weighted graph G and a list of source–sink pairs of terminal vertices of G , the minimum multicut problem consists in selecting a minimum weight set of edges of G whose removal leaves no path from the i th source to the i th sink, for each i . Few tractable special cases are known for this problem. In this paper, we give a simple polynomial-time algorithm solving it in undirected planar graphs where (I) all the terminals lie on the outer face and (II) there is a bounded number of terminals.