Improved Distributed Δ-Coloring

03/08/2018

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by   Mohsen Ghaffari, et al.

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We present a randomized distributed algorithm that computes a Δ-coloring in any non-complete graph with maximum degree Δ≥ 4 in O(Δ) + 2^O(√( n)) rounds, as well as a randomized algorithm that computes a Δ-coloring in O(( n)^2) rounds when Δ∈ [3, O(1)]. Both these algorithms improve on an O(^3 n/Δ)-round algorithm of Panconesi and Srinivasan [STOC'1993], which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an Ω( n) round lower bound of Brandt et al. [STOC'16].