Dynamic Graph Coloring

Luis Barba, Jean Cardinal, Matias Korman, Stefan Langerman, André van Renssen, Marcel Roeloffzen, Sander Verdonschot

Research output: Contribution to journalArticle

Abstract

In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve different trade-offs between the number of recolorings and the number of colors used. For any d> 0 , the first algorithm maintains a proper O(CdN 1 / d ) -coloring while recoloring at most O(d) vertices per update, where C and N are the maximum chromatic number and maximum number of vertices, respectively. The second algorithm reverses the trade-off, maintaining an O(Cd) -coloring with O(dN 1 / d ) recolorings per update. The two converge when d= log N, maintaining an O(Clog N) -coloring with O(log N) recolorings per update. We also present a lower bound, showing that any algorithm that maintains a c-coloring of a 2-colorable graph on N vertices must recolor at least Ω(N2c(c-1)) vertices per update, for any constant c≥ 2.

Original languageEnglish
Pages (from-to)1319-1341
Number of pages23
JournalAlgorithmica
Volume81
Issue number4
DOIs
Publication statusPublished - 2019 Apr 1

Keywords

  • Amortized algorithms
  • Data structures
  • Dynamic coloring
  • Graphs

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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  • Cite this

    Barba, L., Cardinal, J., Korman, M., Langerman, S., van Renssen, A., Roeloffzen, M., & Verdonschot, S. (2019). Dynamic Graph Coloring. Algorithmica, 81(4), 1319-1341. https://doi.org/10.1007/s00453-018-0473-y