{
  "id": "1912.02814",
  "version": "v1",
  "published": "2019-12-05T18:57:01.000Z",
  "updated": "2019-12-05T18:57:01.000Z",
  "title": "Efficient Deterministic Distributed Coloring with Small Bandwidth",
  "authors": [
    "Philipp Bamberger",
    "Fabian Kuhn",
    "Yannic Maus"
  ],
  "categories": [
    "cs.DC",
    "cs.DS"
  ],
  "abstract": "We show that the $(degree+1)$-list coloring problem can be solved deterministically in $O(D \\cdot \\log n \\cdot\\log^3 \\Delta)$ in the CONGEST model, where $D$ is the diameter of the graph, $n$ the number of nodes, and $\\Delta$ is the maximum degree. Using the network decomposition algorithm from Rozhon and Ghaffari this implies the first efficient deterministic, that is, $\\text{poly}\\log n$-time, CONGEST algorithm for the $\\Delta+1$-coloring and the $(degree+1)$-list coloring problem. Previously the best known algorithm required $2^{O(\\sqrt{\\log n})}$ rounds and was not based on network decompositions. Our results also imply deterministic $O(\\log^3 \\Delta)$-round algorithms in MPC and the CONGESTED CLIQUE.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-05T18:57:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "efficient deterministic distributed coloring",
      "small bandwidth",
      "list coloring problem",
      "first efficient deterministic",
      "network decomposition algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}