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European Symposium on Algorithms

ESA 2009: Algorithms - ESA 2009 pp 11–22Cite as

Efficient Computation of the Characteristic Polynomial of a Tree and Related Tasks

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5757))

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.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering Pennsylvania State University, University Park, PA 16802,USA Visiting: ALGO EPFL 1015 Lausanne, Switzerland

    Martin Fürer

  2. Institut für Mathemtik, Universität Zürich, CH-8057, Zrich, Switzerland

    Martin Fürer

Authors
  1. Martin Fürer
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Editor information

Editors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Amos Fiat

  2. Fakultät für Informatik, Universität Karlsruhe (TH), Am Fasanengarten 5, 76131, Karlsruhe, Germany

    Peter Sanders

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© 2009 Springer-Verlag Berlin Heidelberg

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Fürer, M. (2009). Efficient Computation of the Characteristic Polynomial of a Tree and Related Tasks. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-04128-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04127-3

  • Online ISBN: 978-3-642-04128-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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