{
  "id": "1605.04000",
  "version": "v1",
  "published": "2016-05-12T22:40:03.000Z",
  "updated": "2016-05-12T22:40:03.000Z",
  "title": "A short proof that NMF is NP-hard",
  "authors": [
    "Yaroslav Shitov"
  ],
  "comment": "2 pages",
  "categories": [
    "math.CO",
    "cs.CC"
  ],
  "abstract": "We give a short combinatorial proof that the nonnegative matrix factorization is an NP-hard problem. Moreover, we prove that NMF remains NP-hard when restricted to 01-matrices, answering a recent question of Moitra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-12T22:40:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "short proof",
      "short combinatorial proof",
      "nmf remains np-hard",
      "np-hard problem",
      "nonnegative matrix factorization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}