Approximate Counting of Matchings in $(3,3)$-Hypergraphs
Combinatorics
2017-10-26 v3 Data Structures and Algorithms
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 -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 -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
Cite
@article{arxiv.1402.6190,
title = {Approximate Counting of Matchings in $(3,3)$-Hypergraphs},
author = {Andrzej Dudek and Marek Karpinski and Andrzej Ruciński and Edyta Szymańska},
journal= {arXiv preprint arXiv:1402.6190},
year = {2017}
}
Comments
We thank Michael Simkin who pointed out and fixed an error (cf. Lemma 3 and the proof of Claim 7) in an earlier version of this paper