{
  "id": "1905.07547",
  "version": "v1",
  "published": "2019-05-18T07:41:26.000Z",
  "updated": "2019-05-18T07:41:26.000Z",
  "title": "Kantorovich distance on a weighted graph",
  "authors": [
    "Luigi Montrucchio",
    "Giovanni Pistone"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The computation of the Kantorovich distance (1-Wasserstein distance) on a finite state space may be a computationally hard problem in the case of a general distance. In this paper, we derive a simple closed form in the case of the geodesic distance on a weighted tree. Moreover, when the ground distance is defined by a graph, we show that the Kantorovich distance is the minimum of the distances on the spanning trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-18T07:41:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kantorovich distance",
      "weighted graph",
      "finite state space",
      "computationally hard problem",
      "ground distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}