A fast distributed algorithm for (Δ + 1)-edge-coloring

We present a deterministic distributed algorithm in the LOCAL model that finds a proper (Δ+1)-edge-coloring of an n-vertex graph of maximum degree Δ in poly(Δ,log⁡n) rounds. This is the first nontrivial distributed edge-coloring algorithm that uses only Δ+1 colors (matching the bound given by Vizing...

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Vydáno v:Journal of combinatorial theory. Series B Ročník 152; s. 319 - 352
Hlavní autor: Bernshteyn, Anton
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.01.2022
Témata:
Distributed algorithms
Edge-coloring
LOCAL model
Vizing's theorem
Edge-coloring
LOCAL model
Vizing's theorem
Distributed algorithms
ISSN:0095-8956, 1096-0902
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Shrnutí:We present a deterministic distributed algorithm in the LOCAL model that finds a proper (Δ+1)-edge-coloring of an n-vertex graph of maximum degree Δ in poly(Δ,log⁡n) rounds. This is the first nontrivial distributed edge-coloring algorithm that uses only Δ+1 colors (matching the bound given by Vizing's theorem). Our approach is inspired by the recent proof of the measurable version of Vizing's theorem due to Grebík and Pikhurko.
ISSN:0095-8956
1096-0902
DOI:10.1016/j.jctb.2021.10.004