### Abstract

An O(n log^{2} n) algorithm is presented to compute the characteristic polynomial of a tree on n vertices improving on the previously best quadratic time. With the same running time, the algorithm can be generalized in two directions. The algoritm is a counting algorithm, and the same ideas can be used to count other objects. For example, one can count the number of independent sets of all possible sizes simultaneously with the same running time. These counting algorithms not only work for trees, but can be extended to arbitrary graphs of bounded tree-width.

Original language | English (US) |
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Title of host publication | Algorithms - ESA 2009 - 17th Annual European Symposium, Proceedings |

Pages | 11-22 |

Number of pages | 12 |

DOIs | |

State | Published - Nov 2 2009 |

Event | 17th Annual European Symposium on Algorithms, ESA 2009 - Copenhagen, Denmark Duration: Sep 7 2009 → Sep 9 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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Volume | 5757 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th Annual European Symposium on Algorithms, ESA 2009 |
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Country | Denmark |

City | Copenhagen |

Period | 9/7/09 → 9/9/09 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Fürer, M. (2009). Efficient computation of the characteristic polynomial of a tree and related tasks. In

*Algorithms - ESA 2009 - 17th Annual European Symposium, Proceedings*(pp. 11-22). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5757 LNCS). https://doi.org/10.1007/978-3-642-04128-0_2