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Distributed Arboricity-Dependent Graph Coloring via All-to-All Communication

Authors Mohsen Ghaffari, Ali Sayyadi

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Author Details

Mohsen Ghaffari
  • ETH Zurich, Switzerland
Ali Sayyadi
  • Sharif University of Technology, Iran

Funding

The first author acknowledges the support of the Swiss National Foundation, under project number 200021_184735. The second author is grateful for the support of the Student Summer Research Fellowship (SSRF) program at the Computer Science department of ETH Zurich; this project was initiated during an undergraduate internship in the summer of 2018.

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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) https://doi.org/10.4230/LIPIcs.ICALP.2019.142

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)}.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • Distributed Computing
  • Message Passing Algorithms
  • Graph Coloring
  • Arboricity
  • Congested Clique Model
  • Randomized Algorithms

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