Nearly optimal distributed edge colouring in O(log log n) rounds

An extremely simple distributed randomized edge colouring algorithm is given which produces with high probability a proper edge colouring of a given graph G using (1 + {epsilon}){Delta} (G) colours, for any {epsilon} > 0. The algorithm is very fast. In particular, for graphs with sufficiently large vertex degrees (larger than polylog n, but smaller than any positive power of n), the algorithm requires only O(log log n) communication rounds. The algorithm is inherently distributed, but can be implemented on the PRAM, where it requires O(m{Delta}) processors and O(log {Delta} log log n) time, or in a sequential setting, where it requires O(m{Delta}) time.

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