# Fixed-parameter tractability of multicut parameterized by the size of the cutset

Marx, D. and Razgon, Igor
(2011)
Fixed-parameter tractability of multicut parameterized by the size of the cutset.
In:
UNSPECIFIED (ed.)
*Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11.*
New York, U.S.:
ACM Press, pp. 469-478.
ISBN 9781450306911.

## Abstract

Given an undirected graph $G$, a collection {(s1,t1), ..., (sl,tl)} of pairs of vertices, and an integer p, the Edge Multicut problem ask if there is a set S of at most p edges such that the removal of S disconnects every si from the corresponding ti. Vertex Multicut is the analogous problem where S is a set of at most p vertices. Our main result is that both problems can be solved in time 2O(p3) ⋅ nO(1), i.e., fixed-parameter tractable parameterized by the size p of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form f(p) ⋅ nO(1) exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset.

## Metadata

Item Type: | Book Section |
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School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |

Depositing User: | Administrator |

Date Deposited: | 11 Jun 2013 12:41 |

Last Modified: | 09 Aug 2023 12:33 |

URI: | https://eprints.bbk.ac.uk/id/eprint/7444 |

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