Distributed Edge Coloring in Time Polylogarithmic in Δ
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We provide new deterministic algorithms for the edge coloring problem, which is one of the classic and highly studied distributed local symmetry breaking problems. As our main result, we show that a (2Δ-1)-edge coloring can be computed in time polylogΔ + O(log^* n) in the LOCAL model. This improves a result of Balliu, Kuhn, and Olivetti [PODC '20], who gave an algorithm with a quasi-polylogarithmic dependency on Δ. We further show that in the CONGEST model, an (8+ε)Δ-edge coloring can be computed in polylogΔ + O(log^* n) rounds. The best previous O(Δ)-edge coloring algorithm that can be implemented in the CONGEST model is by Barenboim and Elkin [PODC '11] and it computes a 2^O(1/ε)Δ-edge coloring in time O(Δ^ε + log^* n) for any ε∈(0,1].
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