# An O* (1.84k) parameterized algorithm for the multiterminal cut problem

Cao, Yixin and Chen, J and Fan, J
(2014)
*An O* (1.84k) parameterized algorithm for the multiterminal cut problem.*
INFORMATION PROCESSING LETTERS, 114 (4).
pp. 167-173.
ISSN 0020-0190
MTMT:2506564; doi:10.1016/j.ipl.2013.12.001

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## 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: maximum volume minimum(s, t) -cuts by Ford and Fulkerson [11] and isolating cuts by Dahlhaus et al. [9]. 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 {dot operator} nO (1) time, thereby breaking the 2k {dot operator} nO (1) barrier. As a by-product, it gives a 1.36k {dot operator} nO (1) time algorithm for 3-terminal cut. The preprocessing applied on non-terminal vertices might be of use for study of this problem from other aspects. © 2013 Elsevier B.V.

Item Type: | ISI Article |
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Uncontrolled Keywords: | Parameterized computation, Graph algorithms |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

SWORD Depositor: | MTMT Injector |

Depositing User: | EPrints Admin |

Date Deposited: | 05 Feb 2014 12:40 |

Last Modified: | 05 Feb 2014 15:45 |

URI: | https://eprints.sztaki.hu/id/eprint/7524 |

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