Departmental Papers (CIS)

Date of this Version

March 2006

Document Type

Journal Article

Comments

Copyright SIAM, 2006. Reprinted in SIAM Journal on Discrete Mathematics, Volume 20, Issue 1, 2006, pages 261-271.

Abstract

We consider the Steiner k-cut problem which generalizes both the k-cut problem and the multiway cut problem. The Steiner k-cut problem is defined as follows. Given an edge-weighted undirected graph G = (V,E), a subset of vertices X ⊆ V called terminals, and an integer k ≤ |X|, the objective is to find a minimum weight set of edges whose removal results in k disconnected components, each of which contains at least one terminal. We give two approximation algorithms for the problem: a greedy (2 − 2/k )-approximation based on Gomory–Hu trees, and a (2 − 2/|X|)-approximation based on rounding a linear program. We use the insight from the rounding to develop an exact bidirected formulation for the global minimum cut problem (the k-cut problem with k = 2).

Keywords

multiway cut, k-cut, Steiner tree, minimum cut, linear program, approximation algorithm

Share

COinS
 

Date Posted: 20 August 2006

This document has been peer reviewed.