We consider the Steiner k-cut problem, which is a common generalization of the k-cut problem and the multiway cut problem: 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 2 - 2/k-approximation based on Gomory-Hu trees, and a 2 - 2/|X|-approximation based on LP rounding. The latter algorithm is based on roundihg a generalization of a linear programming relaxation suggested by Naor and Rabani [8]. The rounding uses the Goemans and Williamson primal-dual algorithm (and analysis) for the Steiner tree problem [4] in an interesting way and differs from the rounding in [8]. 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). © Springer-Verlag Berlin Heidelberg 2003.
CITATION STYLE
Chekuri, C., Guha, S., & Naor, J. (2003). Approximating Steiner k-cuts. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2719, 189–199. https://doi.org/10.1007/3-540-45061-0_17
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