{
  "annotation_id": "4ad82c42-1711-49d0-bf57-bc9ae2aa7e17",
  "date_created": "2026-03-02T18:02:19.900000Z",
  "date_modified": "2026-03-02T18:02:19.900000Z",
  "file_hash": "c3c98c0946a827bff28901533a78a8648fd210eecf14abc7ea63b627214369e6",
  "private": false,
  "record": {
    "abstract": "We present quantum algorithms for the following graph problems: finding a\nmaximal bipartite matching in time O(n sqrt{m+n} log n), finding a maximal\nnon-bipartite matching in time O(n^2 (sqrt{m/n} + log n) log n), and finding a\nmaximal flow in an integer network in time O(min(n^{7/6} sqrt m * U^{1/3},\nsqrt{n U} m) log n), where n is the number of vertices, m is the number of\nedges, and U \u003c= n^{1/4} is an upper bound on the capacity of an edge.",
    "arxiv_id": "quant-ph/0508205",
    "authors": [
      "Andris Ambainis",
      "Robert Spalek"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Algorithms for Matching and Network Flows",
    "url": "https://arxiv.org/abs/quant-ph/0508205"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "49b2e37d-63d4-419b-824e-60c21734d180",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}