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DOI: 10.4230/LIPIcs.MFCS.2024.33

First-Fit Coloring of Forests in Random Arrival Model

Authors: Bartłomiej Bosek, Grzegorz Gutowski, Michał Lasoń, and Jakub Przybyło

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract

We consider a graph coloring algorithm that processes vertices in order taken uniformly at random and assigns colors to them using First-Fit strategy. We show that this algorithm uses, in expectation, at most (1+o(1))⋅ln n / ln ln n different colors to color any forest with n vertices. We also construct a family of forests that shows that this bound is best possible.

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Bartłomiej Bosek, Grzegorz Gutowski, Michał Lasoń, and Jakub Przybyło. First-Fit Coloring of Forests in Random Arrival Model. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 33:1-33:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bosek_et_al:LIPIcs.MFCS.2024.33,
  author =	{Bosek, Bart{\l}omiej and Gutowski, Grzegorz and Laso\'{n}, Micha{\l} and Przyby{\l}o, Jakub},
  title =	{{First-Fit Coloring of Forests in Random Arrival Model}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{33:1--33:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.33},
  URN =		{urn:nbn:de:0030-drops-205892},
  doi =		{10.4230/LIPIcs.MFCS.2024.33},
  annote =	{Keywords: First-Fit, Online Algorithms, Graph Coloring, Random Arrival Model}
}

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First-Fit Coloring of Forests in Random Arrival Model

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