The Complexity of Multiterminal Cuts
SIAM Journal on Computing
An improved approximation algorithm for multiway cut
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Rounding algorithms for a geometric embedding of minimum multiway cut
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A polynomial-time approximation scheme for planar multiway cut
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximating a class of classification problems
Efficient Approximation and Online Algorithms
Generating partitions of a graph into a fixed number of minimum weight cuts
Discrete Optimization
Minimizing Energies with Hierarchical Costs
International Journal of Computer Vision
Solving planar k-terminal cut in O(nc√k) time
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Simplex partitioning via exponential clocks and the multiway cut problem
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Given an undirected graph G = (V,E) and three specified terminal nodes t1, t2, t3, a 3-cut is a subset A of E such that no two terminals are in the same component of G\A. If a non-negative edge weight ce is specified for each e ∈ E, the optimal 3-cut problem is to find a 3-cut of minimum total weight. This problem is NP-hard, and in fact, is max-SNP-hard. An approximation algorithm having performance guarantee 7/6 has recently been given by Călinescu, Karloff, and Rabani. It is based on a certain linear programming relaxation, for which it is shown that the optimal 3-cut has weight at most 7/6 times the optimal LP value. It is proved here that 7/6 can be improved to 12/11, and that this is best possible. As a consequence, we obtain an approximation algorithm for the optimal 3-cut problem having performance guarantee 12/11.