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An Optimal Decentralized (Δ + 1)-Coloring Algorithm
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28th Annual European Symposium on Algorithms (ESA 2020)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: European Symposium on Algorithms (ESA) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2020-08-26
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Daniel Bertschinger, Johannes Lengler, Anders Martinsson, Robert Meier, Angelika Steger, Miloš Trujić, and Emo Welzl. An Optimal Decentralized (Δ + 1)-Coloring Algorithm. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ESA.2020.17
Abstract
Consider the following simple coloring algorithm for a graph on n vertices. Each vertex chooses a color from {1, ..., Δ(G) + 1} uniformly at random. While there exists a conflicted vertex choose one such vertex uniformly at random and recolor it with a randomly chosen color. This algorithm was introduced by Bhartia et al. [MOBIHOC'16] for channel selection in WIFI-networks. We show that this algorithm always converges to a proper coloring in expected O(n log Δ) steps, which is optimal and proves a conjecture of Chakrabarty and de Supinski [SOSA'20].
Subject Classification
ACM Subject Classification
- Theory of computation → Distributed algorithms
- Mathematics of computing → Graph algorithms
- Mathematics of computing → Graph coloring
- Mathematics of computing → Probabilistic algorithms
Keywords
- Decentralized Algorithm
- Distributed Computing
- Graph Coloring
- Randomized Algorithms
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References
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