Departmental Papers (CIS)

Date of this Version

March 2006

Document Type

Journal Article


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


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).


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



Date Posted: 20 August 2006

This document has been peer reviewed.