The Complexity of Multiterminal Cuts

Authors:
E. Dahlhaus;D. S. Johnson;C. H. Papadimitriou;P. D. Seymour;M. Yannakakis
Affiliations:
-;-;-;-;-
Venue:
SIAM Journal on Computing
Year:
1994

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Abstract

In the multiterminal cut problem one is given an edge-weighted graph and a subset of the vertices called terminals, and is 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 mincut, max-flow problem, and can be solved in polynomial time. It is shown 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. A simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of $2-2/k$ of the optimal cut weight is also described.