{
  "id": "1702.05141",
  "version": "v1",
  "published": "2017-02-16T20:03:34.000Z",
  "updated": "2017-02-16T20:03:34.000Z",
  "title": "L-Infinity optimization to Bergman fans of matroids with an application to phylogenetics",
  "authors": [
    "Daniel Irving Bernstein"
  ],
  "comment": "All results in this submission have already appeared in arXiv:1612.06797 which is being split into two papers (this is one of them)",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a dissimilarity map $\\delta$ on finite set $X$, we show that the set of ultrametrics (equidistant tree metrics) which are $l^\\infty$-nearest to $\\delta$ is a tropical polytope. We give an algorithm for computing a superset of its tropical vertices. It was shown by Ardila that the set of all ultrametrics on a finite set of size $n$ is the Bergman fan associated to the matroid underlying the complete graph on $n$ vertices. Therefore, we derive our results in the more general context of Bergman fans of matroids. This more general context allows our algorithm to be applied to dissimilarity maps where only a subset of the entries are known.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-16T20:03:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bergman fan",
      "l-infinity optimization",
      "application",
      "phylogenetics",
      "dissimilarity map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}