{
  "id": "1907.02673",
  "version": "v1",
  "published": "2019-07-05T04:29:49.000Z",
  "updated": "2019-07-05T04:29:49.000Z",
  "title": "Discrete Decreasing Minimization, Part III: Network Flows",
  "authors": [
    "András Frank",
    "Kazuo Murota"
  ],
  "comment": "23 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A strongly polynomial algorithm is developed for finding an integer-valued feasible $st$-flow of given flow-amount which is decreasingly minimal on a specified subset $F$ of edges in the sense that the largest flow-value on $F$ is as small as possible, within this, the second largest flow-value on $F$ is as small as possible, within this, the third largest flow-value on $F$ is as small as possible, and so on. A characterization of the set of these $st$-flows gives rise to an algorithm to compute a cheapest $F$-decreasingly minimal integer-valued feasible $st$-flow of given flow-amount.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-05T04:29:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C27",
      "90C10",
      "90C25"
    ],
    "keywords": [
      "discrete decreasing minimization",
      "network flows",
      "decreasingly minimal",
      "third largest flow-value",
      "second largest flow-value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}