A Parallel MCMC Algorithm for the Balanced Graph Coloring Problem

  • Donatello Conte
  • Giuliano Grossi
  • Raffaella Lanzarotti
  • Jianyi LinEmail author
  • Alessandro Petrini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11510)


In parallel computation domain, graph coloring is widely studied in its own and represents a reference problem for scheduling of parallel tasks. Unfortunately, common graph coloring strategies usually focus on minimizing the number of colors without any concern for the sizes of each color class, thus producing highly skewed color class distributions. However, to guarantee efficiency in parallel computations, but also in other application contexts, it is important to keep the color classes highly balanced in their sizes. In this paper we address this challenging issue for large scale graphs, proposing a fast parallel MCMC heuristic for sparse graphs that randomly generates good balanced colorings provided that a sufficient number of colors are made available. We show its effectiveness through some numerical simulations on random graphs.


Balanced graph coloring Markov Chain Monte Carlo method Greedy colorer Parallel algorithms 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Donatello Conte
    • 1
  • Giuliano Grossi
    • 2
  • Raffaella Lanzarotti
    • 2
  • Jianyi Lin
    • 3
    Email author
  • Alessandro Petrini
    • 2
  1. 1.Université de Tours, Computer Science Laboratory (LIFAT - EA6300)ToursFrance
  2. 2.Dipartimento di InformaticaUniversità degli Studi di MilanoMilanItaly
  3. 3.Department of MathematicsKhalifa University of Science and TechnologyAbu DhabiUnited Arab Emirates

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