{
  "id": "1204.6422",
  "version": "v1",
  "published": "2012-04-28T16:58:51.000Z",
  "updated": "2012-04-28T16:58:51.000Z",
  "title": "Conflict-free coloring with respect to a subset of intervals",
  "authors": [
    "Panagiotis Cheilaris",
    "Shakhar Smorodinsky"
  ],
  "categories": [
    "math.CO",
    "cs.DM",
    "cs.DS"
  ],
  "abstract": "Given a hypergraph H = (V, E), a coloring of its vertices is said to be conflict-free if for every hyperedge S \\in E there is at least one vertex in S whose color is distinct from the colors of all other vertices in S. The discrete interval hypergraph Hn is the hypergraph with vertex set {1,...,n} and hyperedge set the family of all subsets of consecutive integers in {1,...,n}. We provide a polynomial time algorithm for conflict-free coloring any subhypergraph of Hn, we show that the algorithm has approximation ratio 2, and we prove that our analysis is tight, i.e., there is a subhypergraph for which the algorithm computes a solution which uses twice the number of colors of the optimal solution. We also show that the problem of deciding whether a given subhypergraph of Hn can be colored with at most k colors has a quasipolynomial time algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-28T16:58:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conflict-free coloring",
      "discrete interval hypergraph hn",
      "quasipolynomial time algorithm",
      "subhypergraph",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.6422C"
    }
  }
}