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)


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 3 k/2 or 5 mk/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.


Dynamic Programming Hamiltonian Path Space Polynomial Counting Problem Information Processing Letter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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