# Constant ratio fixed-parameter approximation of the edge multicut problem

Marx, D. and Razgon, Igor
(2009)
Constant ratio fixed-parameter approximation of the edge multicut problem.
*Information Processing Letters* 109
(20),
pp. 1161-1166.
ISSN 0020-0190.

## Abstract

The input of the Edge Multicut problem consists of an undirected graph G and pairs of terminals {s1,t1},…,{sm,tm}; the task is to remove a minimum set of edges such that si and ti are disconnected for every 1⩽i⩽m. The parameterized complexity of the problem, parameterized by the maximum number k of edges that are allowed to be removed, is currently open. The main result of the paper is a parameterized 2-approximation algorithm: in time f(k)⋅nO(1), we can either find a solution of size 2k or correctly conclude that there is no solution of size k. The proposed algorithm is based on a transformation of the Edge Multicut problem into a variant of the parameterized Max-2SAT problem, where the parameter is related to the number of clauses that are not satisfied. It follows from previous results that the latter problem can be 2-approximated in a fixed-parameter time; on the other hand, we show here that it is W[1]-hard. Thus the additional contribution of the present paper is introducing the first natural W[1]-hard problem that is constant-ratio fixed-parameter approximable.

## Metadata

Item Type: | Article |
---|---|

Keyword(s) / Subject(s): | fixed-parameter algorithms, parameterized approximation, multicut, satisfiability problems, graph algorithms |

School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |

Depositing User: | Sarah Hall |

Date Deposited: | 01 Aug 2013 15:44 |

Last Modified: | 09 Aug 2023 12:34 |

URI: | https://eprints.bbk.ac.uk/id/eprint/7923 |

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