Minimum multicuts and Steiner forests for Okamura-Seymour graphs

We study the problem of finding minimum multicuts for an undirected planar graph, where all the terminal vertices are on the boundary of the outer face. This is known as an Okamura-Seymour instance. We show that for such an instance, the minimum multicut problem can be reduced to the minimum-cost Steiner forest problem on a suitably defined dual graph. The minimum-cost Steiner forest problem has a 2-approximation algorithm. Hence, the minimum multicut problem has a 2-approximation algorithm for an Okamura-Seymour instance.