A polynomial algorithm for the k-cut problem for fixed k
Mathematics of Operations Research
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Finding $k$ Cuts within Twice the Optimal
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
A new approach to the minimum cut problem
Journal of the ACM (JACM)
Rounding algorithms for a geometric embedding of minimum multiway cut
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
An improved approximation algorithm for MULTIWAY CUT
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Tree packing and approximating k-cuts
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
Approximating k-cuts via network strength
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
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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 ofv ertices 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 ofwhic h 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 rounding 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).