Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems

  • Authors:

  • M. R. Fellows;C. Knauer;N. Nishimura;P. Ragde;F. Rosamond;U. Stege;D. M. Thilikos;S. Whitesides

  • Affiliations:

  • University of Newcastle, School of Electrical Engineering and Computer Science, Newcastle, Australia;Freie Universität Berlin, Institute of Computer Science, Berlin, Germany;University of Waterloo, School of Computer Science, Waterloo, Canada;University of Waterloo, School of Computer Science, Waterloo, Canada;University of Newcastle, School of Electrical Engineering and Computer Science, Newcastle, Australia;University of Victoria, Department of Computer Science, Victoria, Canada;Universitat Politècnica de Catalunya, Departament de Llenguatges i Sistemes Informàtics, Barcelona, Spain;McGill University, School of Computer Science, Montreal, Canada

  • Venue:
  • Algorithmica - Parameterized and Exact Algorithms
  • Year:
  • 2008

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Abstract

We obtain faster algorithms for problems such as r-dimensional matching and r-set 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). This technique lets us combine Alon, Yuster and Zwick’s color-coding technique with dynamic programming to obtain faster fixed-parameter algorithms for these problems. Our algorithms run in time O(n+2 O(k)), an improvement over previous algorithms for some of these problems running in time O(n+k O(k)). The flexibility of our approach allows tuning of algorithms to obtain smaller constants in the exponent.