Minimum multicuts and Steiner forests for Okamura-Seymour graphs

TL;DR

This paper presents a reduction of the minimum multicut problem in Okamura-Seymour graphs to the Steiner forest problem, enabling a 2-approximation solution for these instances.

Contribution

It introduces a novel reduction technique for minimum multicuts in planar graphs with boundary terminals to Steiner forests, providing an approximation algorithm.

Findings

Minimum multicut problem reduces to Steiner forest in Okamura-Seymour graphs.

The Steiner forest problem admits a 2-approximation algorithm.

This yields a 2-approximation for the multicut problem in these graphs.

Abstract

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.