A simple algorithm for multicuts in planar graphs with outer terminals

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 ith source to the ith 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. (C) 2008 Elsevier B.V. All rights reserved.