Online Edge Coloring via Tree Recurrences and Correlation Decay

Janardhan Kulkarni; Yang P. Liu; Ashwin Sah; Mehtaab Sawhney; Jakub Tarnawski

Online Edge Coloring via Tree Recurrences and Correlation Decay

Data Structures and Algorithms 2021-11-02 v1

Authors: Janardhan Kulkarni , Yang P. Liu , Ashwin Sah , Mehtaab Sawhney , Jakub Tarnawski

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.

Keywords

online edge coloring tree recurrences correlation decay matching locally treelike graphs oblivious adversary

Cite

@article{arxiv.2111.00721,
  title  = {Online Edge Coloring via Tree Recurrences and Correlation Decay},
  author = {Janardhan Kulkarni and Yang P. Liu and Ashwin Sah and Mehtaab Sawhney and Jakub Tarnawski},
  journal= {arXiv preprint arXiv:2111.00721},
  year   = {2021}
}

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22 pages, 1 figure

Online Edge Coloring via Tree Recurrences and Correlation Decay

Abstract

Keywords

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