## Abstract

In the MULTIWAY CUT problem, we are given an undirected edge-weighted graph G=(V,E) with ce denoting the cost (weight) of edge e. We are also given a subset S of V, of size k, called the terminals. The objective is to find a minimum cost set of edges whose removal ensures that the terminals are disconnected. In this paper, we study a bidirected linear programming relaxation of MULTIWAY CUT. We resolve an open problem posed by Vazirani [Approximation Algorithms, first ed., Springer, Berlin, Heidelberg, 2001], and show that the integrality gap of this relaxation is not better than that for a geometric linear programming relaxation given by Cǎlinescu et al. [J. Comput. System Sci. 60(3) (2000) 564-574], and may be strictly worse on some instances.

Original language | English (US) |
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Pages (from-to) | 67-79 |

Number of pages | 13 |

Journal | Discrete Applied Mathematics |

Volume | 150 |

Issue number | 1-3 |

DOIs | |

State | Published - Sep 1 2005 |

## Keywords

- Approximation algorithm
- Bidirected relaxation
- Integrality gap
- MULTIWAY CUT problem

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics