The complexity of multiway cuts (extended abstract). Dahlhaus, E., Johnson, D. S., Papadimitriou, C. H., Seymour, P. D., & Yannakakis, M. In Proc. of ACM Symposium on Theory Of Computing (STOC 1992), pages 241–251, 1992. ACM press, New York.
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},
}