Improved Distributed Δ-Coloring

We present a randomized distributed algorithm that computes a ∆-coloring in any noncomplete graph with maximum degree ∆ ≥ 4 in O(log∆) + 2 √ log logn) rounds, as well as a randomized algorithm that computes a ∆-coloring in O((log logn)) rounds when ∆ ∈ [3, O(1)]. Both these algorithms improve on an O(log n/ log∆)-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(log logn) round lower bound of Brandt et al. [STOC’16]. Supported by ERC Grant No. 336495 (ACDC) and Ulla Tuominen Foundation. Supported by ERC Grant No. 336495 (ACDC)

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