Modifying Colourings Between Time-Steps to Tackle Changes in Dynamic Random Graphs

  • Bradley Hardy
  • Rhyd Lewis
  • Jonathan Thompson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9595)


Many real world operational research problems can be formulated as graph colouring problems. Algorithms for this problem usually operate under the assumption that the size and constraints of a problem are fixed, allowing us to model the problem using a static graph. For many problems however, this is not the case and it would be more appropriate to model such problems using dynamic graphs. In this paper we will explore whether feasible colourings for one graph at time-step t can be modified into a colouring for a similar graph at time-step \(t+1\) in some beneficial manner.


Graph colouring Dynamic graphs Heuristics 


  1. 1.
    Aardal, K.I., Van Hoesel, S.P., Koster, A.M., Mannino, C., Sassano, A.: Models and solution techniques for frequency assignment problems. Ann. Oper. Res. 153(1), 79–129 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Blöchliger, I., Zufferey, N.: A graph coloring heuristic using partial solutions and a reactive tabu scheme. Comput. Oper. Res. 35(3), 960–975 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Chaitin, G.J.: Register allocation & spilling via graph coloring. ACM Sigplan Not. 17(6), 98–101 (1982)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Dupont, A., Linhares, A.C., Artigues, C., Feillet, D., Michelon, P., Vasquez, M.: The dynamic frequency assignment problem. Eur. J. Oper. Res. 195(1), 75–88 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Erben, W.: A grouping genetic algorithm for graph colouring and exam timetabling. In: Burke, E., Erben, W. (eds.) PATAT 2000. LNCS, vol. 2079, pp. 132–156. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Gyárfás, A., Lehel, J.: On-line and first fit colorings of graphs. J. Graph Theor. 12(2), 217–227 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Harary, F., Gupta, G.: Dynamic graph models. Math. Comput. Model. 25(7), 79–87 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Hertz, A., de Werra, D.: Using tabu search techniques for graph coloring. Computing 39(4), 345–351 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Johnson, D.S., Aragon, C.R., McGeoch, L.A., Schevon, C.: Optimization by simulated annealing: an experimental evaluation; part II, graph coloring and number partitioning. Oper. Res. 39(3), 378–406 (1991)CrossRefzbMATHGoogle Scholar
  10. 10.
    Leighton, F.T.: A graph coloring algorithm for large scheduling problems. J. Res. Nat. Bur. Stand. 84(6), 489–506 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lewis, R.: Constructing wedding seating plans: a tabu subject. In: Proceedings of the International Conference on Genetic and Evolutionary Methods (GEM). The Steering Committee of The World Congress in Computer Science, Computer Engineering and Applied Computing (WorldComp), p. 1 (2013)Google Scholar
  12. 12.
    Lovász, L., Saks, M., Trotter, W.T.: An on-line graph coloring algorithm with sublinear performance ratio. Ann. Discrete Math. 43, 319–325 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Monical, C., Stonedahl, F.: Static vs. dynamic populations in genetic algorithms for coloring a dynamic graph. In: Proceedings of the 2014 Conference on Genetic and Evolutionary Computation, pp. 469–476. ACM (2014)Google Scholar
  14. 14.
    Preuveneers, D., Berbers, Y.: ACODYGRA: an agent algorithm for coloring dynamic graphs. Symbolic Numer. Algorithms Sci. Comput. 6, 381–390 (2004)zbMATHGoogle Scholar
  15. 15.
    Qu, R., Burke, E.K., McCollum, B.: Adaptive automated construction of hybrid heuristics for exam timetabling and graph colouring problems. Eur. J. Oper. Res. 198(2), 392–404 (2009)CrossRefzbMATHGoogle Scholar
  16. 16.
    Tantipathananandh, C., Berger-Wolf, T., Kempe, D.: A framework for community identification in dynamic social networks. In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 717–726. ACM (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of MathematicsCardiff UniversityCardiffUK

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