### Abstract

We present a randomized subexponential time, polynomial space parameterized algorithm for the k -Weighted Feedback Arc Set in Tournaments (k -FAST) problem. We also show that our algorithm can be derandomized by slightly increasing the running time. To derandomize our algorithm we construct a new kind of universal hash functions, that we coin universal coloring families. For integers m,k and r, a family of functions from [m] to [r] is called a universal (m,k,r)-coloring family if for any graph G on the set of vertices [m] with at most k edges, there exists an which is a proper vertex coloring of G. Our algorithm is the first non-trivial subexponential time parameterized algorithm outside the framework of bidimensionality.

Original language | English (US) |
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Title of host publication | Automata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings |

Pages | 49-58 |

Number of pages | 10 |

Edition | PART 1 |

DOIs | |

State | Published - Nov 12 2009 |

Externally published | Yes |

Event | 36th International Colloquium on Automata, Languages and Programming, ICALP 2009 - Rhodes, Greece Duration: Jul 5 2009 → Jul 12 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 1 |

Volume | 5555 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 36th International Colloquium on Automata, Languages and Programming, ICALP 2009 |
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Country | Greece |

City | Rhodes |

Period | 7/5/09 → 7/12/09 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Automata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings*(PART 1 ed., pp. 49-58). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5555 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-02927-1_6