Dynamic O(Arboricity) Coloring in Polylogarithmic Worst-Case Time
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3618260.3649782.pdf
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183.64 KB
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Adobe PDF
Checksum (MD5)
e1efa1634e3be8c2f2eb2eabe7bf1a97
Author(s)
Ghaffari, Mohsen
Grunau, Christoph
Date Issued
June 10, 2024
Publisher
ACM|Proceedings of the 56th Annual ACM Symposium on Theory of Computing
Citation
Ghaffari, Mohsen and Grunau, Christoph. 2024. "Dynamic O(Arboricity) Coloring in Polylogarithmic Worst-Case Time."
Version
Final published version
Abstract
A recent work by Christiansen, Nowicki, and Rotenberg [STOC’23] provides dynamic algorithms for coloring sparse graphs, concretely as a function of the graph’s arboricity α. They give two randomized algorithms: O(α logα) implicit coloring in poly(logn) worst-case update and query times, and O(min{α logα, α logloglogn}) implicit coloring in poly(logn) amortized update and query times (against an oblivious adversary). We improve these results in terms of the number of colors and the time guarantee: First, we present an extremely simple algorithm that computes an O(α)-implicit coloring with poly(logn) amortized update and query times. Second, and as the main technical contribution of our work, we show that the time complexity guarantee can be strengthened from amortized to worst-case. That is, we give a dynamic algorithm for implicit O(α)-coloring with poly(logn) worst-case update and query times (against an oblivious adversary).
Description
STOC ’24, June 24–28, 2024, Vancouver, BC, Canada
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1145/3618260.3649782
