{
  "id": "1402.6190",
  "version": "v3",
  "published": "2014-02-25T15:04:21.000Z",
  "updated": "2017-10-25T17:30:14.000Z",
  "title": "Approximate Counting of Matchings in $(3,3)$-Hypergraphs",
  "authors": [
    "Andrzej Dudek",
    "Marek Karpinski",
    "Andrzej Ruciński",
    "Edyta Szymańska"
  ],
  "comment": "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",
  "categories": [
    "math.CO",
    "cs.DS"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-29T07:57:48.000Z",
      "comment": "13 pp, 1 figure",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-10-25T17:30:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hypergraphs",
      "approximate counting",
      "first polynomial time approximation scheme",
      "fully polynomial time approximation scheme",
      "general correlation decay technique"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.6190D"
    }
  }
}