{
  "id": "1112.1139",
  "version": "v1",
  "published": "2011-12-05T15:26:51.000Z",
  "updated": "2011-12-05T15:26:51.000Z",
  "title": "Quantum Verification of Minimum Spanning Tree",
  "authors": [
    "Mark Heiligman"
  ],
  "comment": "5 papges",
  "categories": [
    "quant-ph",
    "cs.DS"
  ],
  "abstract": "Previous studies has shown that for a weighted undirected graph having $n$ vertices and $m$ edges, a minimal weight spanning tree can be found with $O^*(\\sqrt{mn})$ calls to the weight oracle. The present note shows that a given spanning tree can be verified to be a minimal weight spanning tree with only $O(n\\bigr)$ calls to the weight oracle and $O(n+\\sqrt{m}\\log n)$ total work.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-05T15:26:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimum spanning tree",
      "quantum verification",
      "minimal weight spanning tree",
      "weight oracle",
      "total work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1139H"
    }
  }
}