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.Comment: 6 pages, 1 figur