{
  "id": "cond-mat/0001137",
  "version": "v2",
  "published": "2000-01-11T14:58:56.000Z",
  "updated": "2000-05-03T07:08:43.000Z",
  "title": "The number of guards needed by a museum: A phase transition in vertex covering of random graphs",
  "authors": [
    "Martin Weigt",
    "Alexander K. Hartmann"
  ],
  "comment": "4 pages, 3 eps-figures, new version to be published in Phys. Rev. Let",
  "journal": "Phys. Rev. Lett. 84, 6118 (2000)",
  "doi": "10.1103/PhysRevLett.84.6118",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "cs.CC"
  ],
  "abstract": "In this letter we study the NP-complete vertex cover problem on finite connectivity random graphs. When the allowed size of the cover set is decreased, a discontinuous transition in solvability and typical-case complexity occurs. This transition is characterized by means of exact numerical simulations as well as by analytical replica calculations. The replica symmetric phase diagram is in excellent agreement with numerical findings up to average connectivity $e$, where replica symmetry becomes locally unstable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-05-03T07:08:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "phase transition",
      "np-complete vertex cover problem",
      "finite connectivity random graphs",
      "replica symmetric phase diagram"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}