Corpus ID: 211082934

An Optimal Decentralized $(\Delta + 1)$-Coloring Algorithm

@inproceedings{Bertschinger2020AnOD,
  title={An Optimal Decentralized \$(\Delta + 1)\$-Coloring Algorithm},
  author={Daniel Bertschinger and Johannes Lengler and A. Martinsson and Robert Meier and Angelika Steger and Milovs Truji'c and Emo Welzl},
  year={2020}
}
  • Daniel Bertschinger, Johannes Lengler, +4 authors Emo Welzl
  • Published 2020
  • Computer Science, Mathematics
  • Consider the following simple coloring algorithm for a graph on $n$ vertices. Each vertex chooses a color from $\{1, \dotsc, \Delta(G) + 1\}$ 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 $O(n \log \Delta)$ steps… CONTINUE READING

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