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A heuristic algorithm using tree decompositions for the maximum happy vertices problem

Author

Listed:
  • Louis Carpentier

    (KU Leuven Brugge)

  • Jorik Jooken

    (KU Leuven KULAK)

  • Jan Goedgebeur

    (KU Leuven KULAK
    Ghent University)

Abstract

We propose a new methodology to develop heuristic algorithms using tree decompositions. Traditionally, such algorithms construct an optimal solution of the given problem instance through a dynamic programming approach. We modify this procedure by introducing a parameter W that dictates the number of dynamic programming states to consider. We drop the exactness guarantee in favour of a shorter running time. However, if W is large enough such that all valid states are considered, our heuristic algorithm proves optimality of the constructed solution. In particular, we implement a heuristic algorithm for the Maximum Happy Vertices problem using this approach. Our algorithm more efficiently constructs optimal solutions compared to the exact algorithm for graphs of bounded treewidth. Furthermore, our algorithm constructs higher quality solutions than state-of-the-art heuristic algorithms Greedy-MHV and Growth-MHV for instances of which at least 40% of the vertices are initially coloured, at the cost of a larger running time.

Suggested Citation

  • Louis Carpentier & Jorik Jooken & Jan Goedgebeur, 2024. "A heuristic algorithm using tree decompositions for the maximum happy vertices problem," Journal of Heuristics, Springer, vol. 30(1), pages 67-107, April.
    • Handle: RePEc:spr:joheur:v:30:y:2024:i:1:d:10.1007_s10732-023-09522-x
    DOI: 10.1007/s10732-023-09522-x
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    References listed on IDEAS

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    1. 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.
    2. Marco Ghirardi & Fabio Salassa, 2022. "A simple and effective algorithm for the maximum happy vertices problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 181-193, April.
    3. Jorik Jooken & Pieter Leyman & Patrick Causmaecker, 2020. "A multi-start local search algorithm for the Hamiltonian completion problem on undirected graphs," Journal of Heuristics, Springer, vol. 26(5), pages 743-769, October.
    4. Hisao Tamaki, 2019. "Positive-instance driven dynamic programming for treewidth," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1283-1311, May.
    Full references (including those not matched with items on IDEAS)

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