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 -edge coloring can be computed in time 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 . We further show that in the CONGEST model, an -edge coloring can be computed in rounds. The best previous -edge coloring algorithm that can be implemented in the CONGEST model is by Barenboim and Elkin [PODC '11] and it computes a -edge coloring in time for any .
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