In *Proc. of ACM Symposium on Theory Of Computing (STOC 1992)*, pages 241–251, 1992. ACM press, New York.

doi abstract bibtex

doi abstract bibtex

In the Multiway Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the min-cut, max-flow problem, and can be solved in polynomial time. We show that the problem becomes NP-hard as soon as k = 3, but can be solved in polynomial time for planar graphs for any fixed k. The planar problem is NP-hard, however, if k is not fixed. We also describe a simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2ï¿œ2/k of the optimal cut weight.

@InProceedings{dahlhaus92complexity, author = {Dahlhaus, E. and Johnson, D. S. and Papadimitriou, C. H. and Seymour, P. D. and Yannakakis, M.}, title = {The complexity of multiway cuts (extended abstract)}, booktitle = {Proc. of ACM Symposium on Theory Of Computing (STOC 1992)}, year = {1992}, pages = {241--251}, publisher = {ACM press, New York}, abstract = {In the Multiway Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the min-cut, max-flow problem, and can be solved in polynomial time. We show that the problem becomes NP-hard as soon as k = 3, but can be solved in polynomial time for planar graphs for any fixed k. The planar problem is NP-hard, however, if k is not fixed. We also describe a simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2{\"{\i}}{\textquestiondown}{\oe}2/k of the optimal cut weight.}, doi = {10.1145/129712.129736}, isbn = {0-89791-511-9}, location = {Victoria, British Columbia, Canada}, owner = {Sebastian}, timestamp = {2010.10.19}, }

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