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Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
Distributed Arboricity-Dependent Graph Coloring via All-to-All Communication

Authors: Mohsen Ghaffari and Ali Sayyadi

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)


Abstract
We present a constant-time randomized distributed algorithms in the congested clique model that computes an O(alpha)-vertex-coloring, with high probability. Here, alpha 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(alpha)-coloring problem. We also explain that a similar method can provide a constant-time randomized algorithm for decomposing the graph into O(alpha) edge-disjoint forests, so long as alpha <= n^{1-o(1)}.

Cite as

Mohsen Ghaffari and Ali Sayyadi. Distributed Arboricity-Dependent Graph Coloring via All-to-All Communication. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 142:1-142:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{ghaffari_et_al:LIPIcs.ICALP.2019.142,
  author =	{Ghaffari, Mohsen and Sayyadi, Ali},
  title =	{{Distributed Arboricity-Dependent Graph Coloring via All-to-All Communication}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{142:1--142:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.142},
  URN =		{urn:nbn:de:0030-drops-107187},
  doi =		{10.4230/LIPIcs.ICALP.2019.142},
  annote =	{Keywords: Distributed Computing, Message Passing Algorithms, Graph Coloring, Arboricity, Congested Clique Model, Randomized Algorithms}
}
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