### Abstract

We consider the minimum-weight feedback vertex set problem in tournaments: given a tournament with non-negative vertex weights, remove a minimum-weight set of vertices that intersects all cycles. This problem is NP-hard to solve exactly, and Unique Games-hard to approximate by a factor better than 2. We present the first 7/3 approximation algorithm for this problem, improving on the previously best known ratio 5/2 given by Cai et al. [FOCS 1998, SICOMP 2001].

Original language | English |
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Title of host publication | 24th Annual European Symposium on Algorithms (ESA 2016) |

Editors | Piotr Sankowski, Christos Zaroliagis |

Place of Publication | Dagstuhl |

Publisher | Schloss Dagstuhl |

Pages | 67:1-67:14 |

Number of pages | 14 |

Volume | 57 |

DOIs | |

Publication status | Published - 2016 |

### Publication series

Series | Leibniz International Proceedings in Informatics |
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ISSN | 1868-8969 |

## Cite this

Mnich, M., Vassilevska Williams, V., & Végh, L. A. (2016). A 7/3-Approximation for Feedback Vertex Sets in Tournaments. In P. Sankowski, & C. Zaroliagis (Eds.),

*24th Annual European Symposium on Algorithms (ESA 2016)*(Vol. 57, pp. 67:1-67:14). [67] Schloss Dagstuhl. Leibniz International Proceedings in Informatics https://doi.org/10.4230/LIPIcs.ESA.2016.67