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Tackling the maximum happy vertices problem in large networks

Author

Listed:
  • Dhananjay Thiruvady

    (Deakin University)

  • Rhyd Lewis

    (Cardiff University)

  • Kerri Morgan

    (Deakin University)

Abstract

In this paper we consider a variant of graph colouring known as the maximum happy vertices problem. This problem involves taking a graph in which a subset of the vertices have been preassigned to colours. The objective is to then colour the remaining vertices such that the number of happy vertices is maximised, where a vertex is considered happy only when it is assigned to the same colour as all of its neighbours. We design and test a tabu search approach, which is compared to two existing state of the art methods. We see that this new approach is particularly suited to larger problem instances and finds very good solutions in very short time frames. We also propose a algorithm to find upper bounds for the problem efficiently. Moreover, we propose an algorithm for imposing additional precoloured vertices and are hence able to significantly reduce the solution space. Finally, we present an analysis of this problem and use probabilistic arguments to characterise problem hardness.

Suggested Citation

  • Dhananjay Thiruvady & Rhyd Lewis & Kerri Morgan, 2020. "Tackling the maximum happy vertices problem in large networks," 4OR, Springer, vol. 18(4), pages 507-527, December.
    • Handle: RePEc:spr:aqjoor:v:18:y:2020:i:4:d:10.1007_s10288-020-00431-4
    DOI: 10.1007/s10288-020-00431-4
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    References listed on IDEAS

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    1. 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.
    2. Barry McCollum & Andrea Schaerf & Ben Paechter & Paul McMullan & Rhyd Lewis & Andrew J. Parkes & Luca Di Gaspero & Rong Qu & Edmund K. Burke, 2010. "Setting the Research Agenda in Automated Timetabling: The Second International Timetabling Competition," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 120-130, February.
    3. Lewis, R. & Thompson, J., 2015. "Analysing the effects of solution space connectivity with an effective metaheuristic for the course timetabling problem," European Journal of Operational Research, Elsevier, vol. 240(3), pages 637-648.
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