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Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth

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Algorithms - ESA 2009 (ESA 2009)

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

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Abstract

We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobás, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a graph with n vertices given a tree decomposition of the graph of width k. The best previously known result (Courcelle 2008) employs a general logical framework and leads to an algorithm with running time f(k)·n, where f(k) is doubly exponential in k. Analyzing the GF(2)-rank of adjacency matrices in the context of tree decompositions, we give a faster and more direct algorithm. Our algorithm uses \(2^{3k^2+O(k)}\cdot n\) arithmetic operations and can be efficiently implemented in parallel.

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Authors and Affiliations

  1. Saarland University, Germany

    Markus Bläser & Christian Hoffmann

Authors
  1. Markus Bläser
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  2. Christian Hoffmann
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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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Bläser, M., Hoffmann, C. (2009). Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth. 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_56

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  • DOI: https://doi.org/10.1007/978-3-642-04128-0_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04127-3

  • Online ISBN: 978-3-642-04128-0

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