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Faster Dynamic (Δ+1)-Coloring Against Adaptive Adversaries

Authors Maxime Flin , Magnús M. Halldórsson

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  • Theory of computation → Dynamic graph algorithms
Keywords
  • Dynamic Graph Algorithms
  • Coloring

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Abstract

We consider the problem of maintaining a proper (Δ + 1)-vertex coloring in a graph on n-vertices and maximum degree Δ undergoing edge insertions and deletions. We give a randomized algorithm with amortized update time Õ(n^{2/3}) against adaptive adversaries, meaning that updates may depend on past decisions by the algorithm. This improves on the very recent Õ(n^{8/9})-update-time algorithm by Behnezhad, Rajaraman, and Wasim (SODA 2025) and matches a natural barrier for dynamic (Δ+1)-coloring algorithms. The main improvements are on the densest regions of the graph, where we use structural hints from the study of distributed graph algorithms.

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Maxime Flin and Magnús M. Halldórsson. Faster Dynamic (Δ+1)-Coloring Against Adaptive Adversaries. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 79:1-79:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.79

Author Details

Maxime Flin
  • Reykjavik University, Iceland
Magnús M. Halldórsson
  • Reykjavik University, Iceland

Funding

  • Flin, Maxime: Supported by the Icelandic Research Fund Grant No. 2310015-053.
  • Halldórsson, Magnús M.: Supported by the Icelandic Research Fund Grant No. 2511609.

Acknowledgements

Discussions with participants of Dagstuhl Seminar 24471, Graph Algorithms: Distributed Meets Dynamic, served as a key motivation for this work.

References

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