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.
Part of research of the 3rd and 4th authors done at Emory University, Atlanta and another part during their visits to the Institut Mittag-Leffler (Djursholm, Sweden).
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Dudek, A., Karpinski, M., Ruciński, A., Szymańska, E. (2014). Approximate Counting of Matchings in (3,3)-Hypergraphs. In: Ravi, R., Gørtz, I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham. https://doi.org/10.1007/978-3-319-08404-6_33
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DOI: https://doi.org/10.1007/978-3-319-08404-6_33
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