Efficient computation of the characteristic polynomial of a tree and related tasks

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    2 Scopus citations

    Abstract

    An O(n log2 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 languageEnglish (US)
    Title of host publicationAlgorithms - ESA 2009 - 17th Annual European Symposium, Proceedings
    Pages11-22
    Number of pages12
    DOIs
    StatePublished - Nov 2 2009
    Event17th Annual European Symposium on Algorithms, ESA 2009 - Copenhagen, Denmark
    Duration: Sep 7 2009Sep 9 2009

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume5757 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other17th Annual European Symposium on Algorithms, ESA 2009
    CountryDenmark
    CityCopenhagen
    Period9/7/099/9/09

    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