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Distributed arboricity-dependent graph coloring via all-to-all communication

Ghaffari, M ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.4230/LIPIcs.ICALP.2019.142
  3. Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2019
  4. Abstract:
  5. We present a constant-time randomized distributed algorithms in the congested clique model that computes an O(α)-vertex-coloring, with high probability. Here, α denotes the arboricity of the graph, which is, roughly speaking, the edge-density of the densest subgraph. Congested clique is a well-studied model of synchronous message passing for distributed computing with all-to-all communication: per round each node can send one O(log n)-bit message algorithm to each other node. Our O(1)-round algorithm settles the randomized round complexity of the O(α)-coloring problem. We also explain that a similar method can provide a constant-time randomized algorithm for decomposing the graph into O(α) edge-disjoint forests, so long as α ≤ n1−o(1). © Mohsen Ghaffari and Ali Sayyadi; licensed under Creative Commons License CC-BY
  6. Keywords:
  7. Arboricity ; Congested clique model ; Distributed computing ; Graph Coloring ; Message passing algorithms ; Automata theory ; Distributed computer systems ; Graph theory ; All-to-all communication ; Coloring problems ; Graph colorings ; High probability ; Message passing algorithm ; Randomized algorithms ; Randomized distributed algorithms ; Message passing
  8. Source: 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019, 9 July 2019 through 12 July 2019 ; Volume 132 , 2019 ; 18688969 (ISSN); 9783959771092 (ISBN)
  9. URL: https://drops.dagstuhl.de/opus/volltexte/2019/10718