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Tackling the edge dynamic graph colouring problem with and without future adjacency information

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  • Bradley Hardy

    (Cardiff University)

  • Rhyd Lewis

    (Cardiff University)

  • Jonathan Thompson

    (Cardiff University)

Abstract

Many real world operational research problems, such as frequency assignment and exam timetabling, can be reformulated as graph colouring problems (GCPs). Most algorithms for the GCP operate under the assumption that its constraints are fixed, allowing us to model the problem using a static graph. However, in many real-world cases this does not hold and it is more appropriate to model problems with constraints that change over time using an edge dynamic graph. Although exploring methods for colouring dynamic graphs has been identified as an area of interest with many real-world applications, to date, very little literature exists regarding such methods. In this paper we present several heuristic methods for modifying a feasible colouring at time-step t into an initial, but not necessarily feasible, colouring for a “similar” graph at time-step $$t+1$$ t + 1 . We will discuss two cases; (1) where changes occur at random, and (2) where probabilistic information about future changes is provided. Experimental results are also presented and the benefits of applying these particular modification methods are investigated.

Suggested Citation

  • Bradley Hardy & Rhyd Lewis & Jonathan Thompson, 2018. "Tackling the edge dynamic graph colouring problem with and without future adjacency information," Journal of Heuristics, Springer, vol. 24(3), pages 321-343, June.
    • Handle: RePEc:spr:joheur:v:24:y:2018:i:3:d:10.1007_s10732-017-9327-z
    DOI: 10.1007/s10732-017-9327-z
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    References listed on IDEAS

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    1. David S. Johnson & Cecilia R. Aragon & Lyle A. McGeoch & Catherine Schevon, 1991. "Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning," Operations Research, INFORMS, vol. 39(3), pages 378-406, June.
    2. Rhyd Lewis & Fiona Carroll, 2016. "Creating seating plans: a practical application," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(11), pages 1353-1362, November.
    3. Qu, Rong & Burke, Edmund K. & McCollum, Barry, 2009. "Adaptive automated construction of hybrid heuristics for exam timetabling and graph colouring problems," European Journal of Operational Research, Elsevier, vol. 198(2), pages 392-404, October.
    4. Dupont, Audrey & Linhares, Andréa Carneiro & Artigues, Christian & Feillet, Dominique & Michelon, Philippe & Vasquez, Michel, 2009. "The dynamic frequency assignment problem," European Journal of Operational Research, Elsevier, vol. 195(1), pages 75-88, May.
    5. Philippe Galinier & Jin-Kao Hao, 1999. "Hybrid Evolutionary Algorithms for Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 379-397, December.
    6. Karen Aardal & Stan Hoesel & Arie Koster & Carlo Mannino & Antonio Sassano, 2007. "Models and solution techniques for frequency assignment problems," Annals of Operations Research, Springer, vol. 153(1), pages 79-129, September.
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    Cited by:

    1. Can Akkan & Ayla Gülcü & Zeki Kuş, 2022. "Bi-criteria simulated annealing for the curriculum-based course timetabling problem with robustness approximation," Journal of Scheduling, Springer, vol. 25(4), pages 477-501, August.

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