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Approximate Counting of Matchings in (3,3)-Hypergraphs

  • Andrzej Dudek
  • Marek Karpinski
  • Andrzej Ruciński
  • Edyta Szymańska
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)

Abstract

We design a fully polynomial time approximation scheme (FPTAS) for counting the number of matchings (packings) in arbitrary 3-uniform hypergraphs of maximum degree three, referred to as (3,3)-hypergraphs. It is the first polynomial time approximation scheme for that problem, which includes also, as a special case, the 3D Matching counting problem for 3-partite (3,3)-hypergraphs. The proof technique of this paper uses the general correlation decay technique and a new combinatorial analysis of the underlying structures of the intersection graphs. The proof method could be also of independent interest.

Keywords

Intersection Graph Polynomial Time Approximation Scheme Fully Polynomial Time Approximation Scheme Block Graph Simplicial Block 
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 International Publishing Switzerland 2014

Authors and Affiliations

  • Andrzej Dudek
    • 1
  • Marek Karpinski
    • 2
  • Andrzej Ruciński
    • 3
  • Edyta Szymańska
    • 3
  1. 1.Western Michigan UniversityKalamazooUSA
  2. 2.Department of Computer ScienceUniversity of BonnGermany
  3. 3.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznańPoland

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