Counting Paths and Packings in Halves

  • Andreas Björklund
  • Thore Husfeldt
  • Petteri Kaski
  • Mikko Koivisto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5757)

Abstract

We show that one can count k-edge paths in an n-vertex graph and m-set k-packings on an n-element universe, respectively, in time \({n \choose k/2}\) and \({n \choose mk/2}\), up to a factor polynomial in n, k, and m; in polynomial space, the bounds hold if multiplied by 3k/2 or 5mk/2, respectively. These are implications of a more general result: given two set families on an n-element universe, one can count the disjoint pairs of sets in the Cartesian product of the two families with O(n ℓ) basic operations, where ℓ is the number of members in the two families and their subsets.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andreas Björklund
    • 1
  • Thore Husfeldt
    • 1
    • 2
  • Petteri Kaski
    • 3
  • Mikko Koivisto
    • 3
  1. 1.Department of Computer ScienceLund UniversityLundSweden
  2. 2.IT University of CopenhagenKøbenhavn SDenmark
  3. 3.Helsinki Institute for Information Technology HIIT, Department of Computer ScienceUniversity of HelsinkiFinland

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