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Decentralized Distributed Graph Coloring II: Degree+1-Coloring Virtual Graphs

Authors Maxime Flin , Magnús M. Halldórsson , Alexandre Nolin

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Author Details

Maxime Flin
  • Reykjavík University, Iceland
Magnús M. Halldórsson
  • Reykjavík University, Iceland
Alexandre Nolin
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

Funding

  • Flin, Maxime: Icelandic Research Fund (grant 2310015).
  • Halldórsson, Magnús M.: Icelandic Research Fund (grant 217965).

Cite As Get BibTex

Maxime Flin, Magnús M. Halldórsson, and Alexandre Nolin. Decentralized Distributed Graph Coloring II: Degree+1-Coloring Virtual Graphs. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 24:1-24:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.24

Abstract

Graph coloring is fundamental to distributed computing. We give the first general treatment of the coloring of virtual graphs, where the graph H to be colored is locally embedded within the communication graph G. Besides generalizing classical distributed graph coloring (where H = G), this captures other previously studied settings, including cluster graphs and power graphs. 
We find that the complexity of coloring a virtual graph depends linearly on the edge congestion of its embedding. The main question of interest is how fast we can color virtual graphs of constant congestion. We find that, surprisingly, these graphs can be colored nearly as fast as ordinary graphs. Namely, we give a O(log⁴log n)-round algorithm for the deg+1-coloring problem, where each node is assigned more colors than its degree. 
This can be viewed as a case where a distributed graph problem can be solved even when the operation of each node is decentralized.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Mathematics of computing → Graph coloring
Keywords
  • Graph Coloring
  • Distributed Algorithms
  • Virtual Graphs
  • Congestion
  • Dilation

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