A LINEAR-TIME ALGORITHM FOR EDGE-DISJOINT PATHS IN PLANAR GRAPHS

In this paper we discuss the problem of finding edge-disjoint paths in a planar, undirected graph such that each path connects two specified vertices on the boundary of the graph. We will focus on the "classical" case where an instance additionally fulfills the so-called evenness-condition. The fastest algorithm for this problem known from the literature requires O (nb/3(loglogn)l/3) time, where n denotes the number of vertices. In this paper now, we introduce a new approach to this problem, which results in an O(n) algorithm. The proof of correctness immediately yields an alternative proof of the Theorem of Okamura and Seymour, which states a necessary and sufficient condition for solvability

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.Comment: 6 pages, 1 figur