Approximation Algorithms for Some Parameterized Counting Problems

  • V. Arvind
  • Venkatesh Raman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2518)

Abstract

We give a randomized fixed parameter tractable algorithm to approximately count the number of copies of a k-vertex graph with bounded treewidth in an n vertex graph. As a consequence, we get randomized algorithms with running time kO(k)nO(1), approximation ratio 1/kO(k), and error probability 2-no(1) for (a) approximately counting the number of matchings of size k in an n vertex graph and (b) approximately counting the number of paths of length k in an n vertex graph. Our algorithm is based on the Karp-Luby approximate counting technique [8] applied to fixed parameter tractable problems, and the color-coding technique of Alon, Yuster and Zwick [1]. We also show some W-hardness results for parameterized exact counting problems.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • V. Arvind
    • 1
  • Venkatesh Raman
    • 1
  1. 1.The Institute of Mathematical SciencesChennaiIndia

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