Emergent Mind
Online Edge Coloring via Tree Recurrences and Correlation Decay
(2111.00721)
Published Nov 1, 2021
in
cs.DS
Abstract
We give an online algorithm that with high probability computes a $\left(\frac{e}{e-1} + o(1)\right)\Delta$ edge coloring on a graph $G$ with maximum degree $\Delta = \omega(\log n)$ under online edge arrivals against oblivious adversaries, making first progress on the conjecture of Bar-Noy, Motwani, and Naor in this general setting. Our algorithm is based on reducing to a matching problem on locally treelike graphs, and then applying a tree recurrences based approach for arguing correlation decay.
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