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 LP rounding. We use the insight from the rounding to develop an exact bi-directed formulation for the global minimum cut problem (the k-cut problem with k = 2).
The best result known for this problem is a 2 − 2/k approximation algorithm due to Chekuri et al. REF .
The Steiner k-Cut Problem ∗
ICALP
Mathematics Computer Science