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

  • Martin Fürer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

characteristic polynomial counting matchings counting independent sets bounded tree-width efficient algorithms 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Martin Fürer
    • 1
    • 2
  1. 1.Department of Computer Science and Engineering Pennsylvania State University, University Park, PA 16802,USA Visiting: ALGO EPFL 1015 LausanneSwitzerland
  2. 2.Institut für MathemtikUniversität ZürichZrichSwitzerland

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