### 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 language | English (US) |
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Pages (from-to) | 864-894 |

Number of pages | 31 |

Journal | SIAM Journal on Computing |

Volume | 23 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1994 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Mathematics(all)

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## Cite this

*SIAM Journal on Computing*,

*23*(4), 864-894. https://doi.org/10.1137/S0097539792225297