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A Polynomial Algorithm for the Degree-Constrained Minimum K-Tree Problem

Author

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  • Marshall L. Fisher

    (University of Pennsylvania, Philadelphia, Pennsylvania)

Abstract

Given a graph with n + 1 nodes, a K -tree is defined to be a set of n + K edges that span the graph. This paper presents an algorithm for finding a minimum cost K -tree with a specified degree at a designated node. The algorithm runs in O ( n 3 ) time and is useful in the optimal solution of certain Lagrangian relaxations arising in vehicle routing.

Suggested Citation

  • Marshall L. Fisher, 1994. "A Polynomial Algorithm for the Degree-Constrained Minimum K-Tree Problem," Operations Research, INFORMS, vol. 42(4), pages 775-779, August.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:4:p:775-779
    DOI: 10.1287/opre.42.4.775
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    Citations

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    Cited by:

    1. X-Y Li & P Tian & S C H Leung, 2009. "An ant colony optimization metaheuristic hybridized with tabu search for open vehicle routing problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(7), pages 1012-1025, July.
    2. Fung, Richard Y.K. & Liu, Ran & Jiang, Zhibin, 2013. "A memetic algorithm for the open capacitated arc routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 50(C), pages 53-67.
    3. Brandão, José, 2020. "A memory-based iterated local search algorithm for the multi-depot open vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 284(2), pages 559-571.
    4. Brandao, Jose, 2006. "A new tabu search algorithm for the vehicle routing problem with backhauls," European Journal of Operational Research, Elsevier, vol. 173(2), pages 540-555, September.
    5. Martinhon, Carlos & Lucena, Abilio & Maculan, Nelson, 2004. "Stronger K-tree relaxations for the vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 158(1), pages 56-71, October.
    6. Brandao, Jose, 2004. "A tabu search algorithm for the open vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 157(3), pages 552-564, September.

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