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Chandra Chekuri, Sudipto Guha, and Joseph Naor, "The Steiner k-Cut Problem", . March 2006.
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.