License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.160
URN: urn:nbn:de:0030-drops-91640
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9164/
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Parter, Merav

(Delta+1) Coloring in the Congested Clique Model

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LIPIcs-ICALP-2018-160.pdf (0.9 MB)

Abstract

In this paper, we present improved algorithms for the (Delta+1) (vertex) coloring problem in the Congested Clique model of distributed computing. In this model, the input is a graph on n nodes, initially each node knows only its incident edges, and per round each two nodes can exchange O(log n) bits of information.
Our key result is a randomized (Delta+1) vertex coloring algorithm that works in O(log log Delta * log^* Delta)-rounds. This is achieved by combining the recent breakthrough result of [Chang-Li-Pettie, STOC'18] in the {LOCAL} model and a degree reduction technique. We also get the following results with high probability: (1) (Delta+1)-coloring for Delta=O((n/log n)^{1-epsilon}) for any epsilon in (0,1), within O(log(1/epsilon)log^* Delta) rounds, and (2) (Delta+Delta^{1/2+o(1)})-coloring within O(log^* Delta) rounds. Turning to deterministic algorithms, we show a (Delta+1)-coloring algorithm that works in O(log Delta) rounds. Our new bounds provide exponential improvements over the state of the art.

BibTeX - Entry

@InProceedings{parter:LIPIcs:2018:9164,
  author =	{Merav Parter},
  title =	{{(Delta+1) Coloring in the Congested Clique Model}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{160:1--160:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9164},
  URN =		{urn:nbn:de:0030-drops-91640},
  doi =		{10.4230/LIPIcs.ICALP.2018.160},
  annote =	{Keywords: Distributed Graph Algorithms, Coloring, Congested Clique}
}

Keywords: Distributed Graph Algorithms, Coloring, Congested Clique
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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