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First-Fit Coloring of Forests in Random Arrival Model

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

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Author Details

Bartłomiej Bosek
  • Institute of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Grzegorz Gutowski
  • Institute of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Michał Lasoń
  • Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland
Jakub Przybyło
  • AGH University of Krakow, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Kraków, Poland

Funding

  • Bosek, Bartłomiej: Partially supported by grant no. 2023/51/B/ST6/02833 from National Science Centre, Poland.
  • Gutowski, Grzegorz: Partially supported by grant no. 2023/51/B/ST6/02833 from National Science Centre, Poland.
  • Lasoń, Michał: Partially supported by grant no. 2019/34/E/ST1/00087 from National Science Centre, Poland.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.MFCS.2024.33

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.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • First-Fit
  • Online Algorithms
  • Graph Coloring
  • Random Arrival Model

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References

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