Deterministic Edge Coloring with few Colors in CONGEST
Joakim Blikstad, Yannic Maus, Tijn de Vos

TL;DR
This paper introduces a deterministic distributed algorithm in the CONGEST model for edge coloring graphs with near-optimal color bounds, significantly improving round complexity and bridging online and distributed graph coloring techniques.
Contribution
It presents the first polylogarithmic-round CONGEST algorithm for $(1+ ext{epsilon}) imes ext{Delta}+O( ext{sqrt(log n)})$ edge coloring, connecting online and distributed methods.
Findings
Achieves $(1+ ext{epsilon}) imes ext{Delta}+O( ext{sqrt(log n)})$ colors in polylogarithmic rounds.
Improves the complexity of $2 ext{Delta}-1$ edge coloring to $ ilde{O}( ext{log}^{2.5} n+ ext{log}^2 ext{Delta} ext{log} n)$ rounds.
First to surpass classical online lower bounds in the distributed setting.
Abstract
As the main contribution of this work we present deterministic edge coloring algorithms in the CONGEST model. In particular, we present an algorithm that edge colors any -node graph with maximum degree with with colors in rounds. This brings the upper bound polynomially close to the lower bound of rounds that also holds in the more powerful LOCAL model [Chang, He, Li, Pettie, Uitto; SODA'18]. As long as our algorithm uses fewer than colors and to the best of our knowledge is the first polylogarithmic-round CONGEST algorithm achieving this for any range of . As a corollary we also improve the complexity of edge coloring with colors for all ranges of to $\tilde{O}(\log^{2.5} n+\log^2 \Delta…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Limits and Structures in Graph Theory
