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Kernel Bounds for Path and Cycle Problems

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Parameterized and Exact Computation (IPEC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7112))

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Abstract

Connectivity problems like k-Path and k-Disjoint Paths relate to many important milestones in parameterized complexity, namely the Graph Minors Project, color coding, and the recent development of techniques for obtaining kernelization lower bounds. This work explores the existence of polynomial kernels for various path and cycle problems, by considering nonstandard parameterizations. We show polynomial kernels when the parameters are a given vertex cover, a modulator to a cluster graph, or a (promised) max leaf number. We obtain lower bounds via cross-composition, e.g., for Hamiltonian Cycle and related problems when parameterized by a modulator to an outerplanar graph.

This work was supported by the Netherlands Organization for Scientific Research (NWO), project “KERNELS: Combinatorial Analysis of Data Reduction”.

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Authors and Affiliations

  1. Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands

    Hans L. Bodlaender, Bart M. P. Jansen & Stefan Kratsch

Authors
  1. Hans L. Bodlaender
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  2. Bart M. P. Jansen
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  3. Stefan Kratsch
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Editor information

Editors and Affiliations

  1. MTA SZTAKI, Lágymányosi u. 11, 1111, Budapest, Hungary

    Dániel Marx

  2. Lehrgebiet Theoretische Informatik, RWTH Aachen, Ahornstraße 55, 52056, Aachen, Germany

    Peter Rossmanith

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Bodlaender, H.L., Jansen, B.M.P., Kratsch, S. (2012). Kernel Bounds for Path and Cycle Problems. In: Marx, D., Rossmanith, P. (eds) Parameterized and Exact Computation. IPEC 2011. Lecture Notes in Computer Science, vol 7112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28050-4_12

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  • DOI: https://doi.org/10.1007/978-3-642-28050-4_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28049-8

  • Online ISBN: 978-3-642-28050-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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