## Abstract

We study the multiterminal cut problem, which, given an n-vertex graph whose edges are integer-weighted and a set of terminals, asks for a partition of the vertex set such that each terminal is in a distinct part, and the total weight of crossing edges is at most k. Our weapons shall be two classical results known for decades. One is max volume min (s,t)-cuts by [Ford and Fulkerson, Flows in Networks. Princeton University Press, 1962], and the other is isolating cuts by [Dahlhaus et al., The complexity of multiterminal cuts. SIAM J. Comp. 23(4), 1994]. We sharpen these old weapons with the help of submodular functions, and apply them to this problem, which enable us to design a more elaborated branching scheme on deciding whether a non-terminal vertex is with a terminal or not. This bounded search tree algorithm can be shown to run in 1.84k·nO(1), thereby breaking the 2k·nO(1)barrier. As a by-product, it gives a 1.36k·nO(1)algorithm for 3-terminal cut. The preprocessing applied on non-terminal vertices might be of use for study of this problem from other aspects.

Original language | English |
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Title of host publication | Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings |

Pages | 84-94 |

Number of pages | 11 |

DOIs | |

Publication status | Published - 3 Sept 2013 |

Externally published | Yes |

Event | 19th International Symposium on Fundamentals of Computation Theory, FCT 2013 - Liverpool, United Kingdom Duration: 19 Aug 2013 → 21 Aug 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8070 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 19th International Symposium on Fundamentals of Computation Theory, FCT 2013 |
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Country/Territory | United Kingdom |

City | Liverpool |

Period | 19/08/13 → 21/08/13 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science

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