An Optimal Decentralized $(\Delta + 1)$-Coloring Algorithm
Data Structures and Algorithms
2021-05-04 v2 Discrete Mathematics
Combinatorics
Abstract
Consider the following simple coloring algorithm for a graph on vertices. Each vertex chooses a color from 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 steps, which is optimal and proves a conjecture of Chakrabarty and Supinski [SOSA'20].
Cite
@article{arxiv.2002.05121,
title = {An Optimal Decentralized $(\Delta + 1)$-Coloring Algorithm},
author = {Daniel Bertschinger and Johannes Lengler and Anders Martinsson and Robert Meier and Angelika Steger and Miloš Trujić and Emo Welzl},
journal= {arXiv preprint arXiv:2002.05121},
year = {2021}
}