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Parameterized Approximability of the Disjoint Cycle Problem

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Book cover Automata, Languages and Programming (ICALP 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4596))

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Abstract

We give an fpt approximation algorithm for the directed vertex disjoint cycle problem. Given a directed graph G with n vertices and a positive integer k, the algorithm constructs a family of at least k/ρ(k) disjoint cycles of G if the graph G has a family of at least k disjoint cycles (and otherwise may still produce a solution, or just report failure). Here ρ is a computable function such that k/ρ(k) is nondecreasing and unbounded. The running time of our algorithm is polynomial.

The directed vertex disjoint cycle problem is hard for the parameterized complexity class W1, and to the best of our knowledge our algorithm is the first fpt approximation algorithm for a natural W1-hard problem.

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Authors and Affiliations

  1. Institut für Informatik, Humboldt-Universität, Unter den Linden 6, 10099 Berlin, Germany

    Martin Grohe & Magdalena Grüber

Authors
  1. Martin Grohe
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  2. Magdalena Grüber
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Lars Arge Christian Cachin Tomasz Jurdziński Andrzej Tarlecki

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Grohe, M., Grüber, M. (2007). Parameterized Approximability of the Disjoint Cycle Problem. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_33

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  • DOI: https://doi.org/10.1007/978-3-540-73420-8_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73419-2

  • Online ISBN: 978-3-540-73420-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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