Complexity of multiterminal cuts

E. Dahlhaus, D. S. Johnson, C. H. Papadimitriou, P. D. Seymour, M. Yannakakis

Research output: Contribution to journalArticlepeer-review

449 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)864-894
Number of pages31
JournalSIAM Journal on Computing
Volume23
Issue number4
DOIs
StatePublished - 1994
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Mathematics(all)

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