Dynamic Graph Coloring

  • Luis Barba
  • Jean Cardinal
  • Matias Korman
  • Stefan Langerman
  • André van Renssen
  • Marcel Roeloffzen
  • Sander Verdonschot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)

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 \(O(\mathcal {C} dN ^{1/d})\)-coloring while recoloring at most O(d) vertices per update, where \(\mathcal {C} \) and \(N \) are the maximum chromatic number and maximum number of vertices, respectively. The second algorithm reverses the trade-off, maintaining an \(O(\mathcal {C} d)\)-coloring with \(O(dN ^{1/d})\) 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 \(\varOmega (N ^\frac{2}{c(c-1)})\) vertices per update, for any constant \(c \ge 2\).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Luis Barba
    • 1
  • Jean Cardinal
    • 2
  • Matias Korman
    • 3
  • Stefan Langerman
    • 2
  • André van Renssen
    • 4
    • 5
  • Marcel Roeloffzen
    • 4
    • 5
  • Sander Verdonschot
    • 6
  1. 1.Dept. of Computer ScienceETH ZürichZürichSwitzerland
  2. 2.Départment d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium
  3. 3.Tohoku UniversitySendaiJapan
  4. 4.National Institute of InformaticsTokyoJapan
  5. 5.JST, ERATO, Kawarabayashi Large Graph ProjectNational Institute of InformaticsTokyoJapan
  6. 6.School of Computer ScienceCarleton UniversityOttawaCanada

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