Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems

  • Michael R. Fellows
  • C. Knauer
  • N. Nishimura
  • P. Ragde
  • F. Rosamond
  • U. Stege
  • Dimitrios M. Thilikos
  • S. Whitesides
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3221)

Abstract

We obtain faster algorithms for problems such as r-dimensional matching, r-set packing, graph packing, and graph edge packing when the size k of the solution is considered a parameter. We first establish a general framework for finding and exploiting small problem kernels (of size polynomial in k). Previously such a kernel was known only for triangle packing. This technique lets us combine, in a new and sophisticated way, Alon, Yuster and Zwick’s color-coding technique with dynamic programming on the structure of the kernel to obtain faster fixed-parameter algorithms for these problems. Our algorithms run in time O(n+2O(k)), an improvement over previous algorithms for some of these problems running in time O(n+kO(k)). The flexibility of our approach allows tuning of algorithms to obtain smaller constants in the exponent.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Michael R. Fellows
    • 1
  • C. Knauer
    • 2
  • N. Nishimura
    • 3
  • P. Ragde
    • 3
  • F. Rosamond
    • 1
  • U. Stege
    • 4
  • Dimitrios M. Thilikos
    • 5
  • S. Whitesides
    • 6
  1. 1.School of Electrical Engineering and Computer ScienceUniversity of NewcastleAustralia
  2. 2.Institute of Computer ScienceFreie Universität BerlinGermany
  3. 3.School of Computer ScienceUniversity of WaterlooCanada
  4. 4.Department of Computer ScienceUniversity of VictoriaCanada
  5. 5.Departament de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaSpain
  6. 6.School of Computer ScienceMcGill UniversityCanada

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