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International Workshop on Parameterized and Exact Computation

IWPEC 2006: Parameterized and Exact Computation pp 192–202Cite as

The Undirected Feedback Vertex Set Problem Has a Poly(k) Kernel

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4169))

Abstract

Resolving a noted open problem, we show that the Undirected Feedback Vertex Set problem, parameterized by the size of the solution set of vertices, is in the parameterized complexity class Poly(k), that is, polynomial-time pre-processing is sufficient to reduce an initial problem instance (G,k) to a decision-equivalent simplified instance (G′,k′) where k′ ≤k, and the number of vertices of G′ is bounded by a polynomial function of k. Our main result shows an O(k 11) kernelization bound.

This research has been supported in part by the U.S. National Science Foundation under grant CCR–0075792, by the U.S. Office of Naval Research under grant N00014–01–1–0608, by the U.S. Department of Energy under contract DE–AC05–00OR22725, and by the Australian Research Council under the auspices of the Australian Centre for Bioinformatics, through Federation Fellowship support of the first author, and through Discovery Project support of the second and third authors.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Queensland, Brisbane, QLD, 4072

    Kevin Burrage & Shev Mac

  2. Griffith University, Brisbane, QLD, 4111, Australia

    Vladimir Estivill-Castro

  3. School of EE & CS, University of Newcastle, Callaghan, NSW, 2308, Australia

    Michael Fellows

  4. Department of Computer Science, University of Tennessee, Knoxville, TN, 37996-3450, USA

    Michael Langston

  5. Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831-6164, USA

    Michael Langston

  6. The Retreat for the Arts and Sciences, Newcastle, Australia

    Frances Rosamond

Authors
  1. Kevin Burrage
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  2. Vladimir Estivill-Castro
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  3. Michael Fellows
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  4. Michael Langston
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  5. Shev Mac
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  6. Frances Rosamond
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, The Netherlands

    Hans L. Bodlaender

  2. University of Tennessee, 37996-3450, Knoxville, Tennessee, U.S.A.

    Michael A. Langston

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© 2006 Springer-Verlag Berlin Heidelberg

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Burrage, K., Estivill-Castro, V., Fellows, M., Langston, M., Mac, S., Rosamond, F. (2006). The Undirected Feedback Vertex Set Problem Has a Poly(k) Kernel. In: Bodlaender, H.L., Langston, M.A. (eds) Parameterized and Exact Computation. IWPEC 2006. Lecture Notes in Computer Science, vol 4169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11847250_18

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  • DOI: https://doi.org/10.1007/11847250_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-39098-5

  • Online ISBN: 978-3-540-39101-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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