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Maximal Direct Covering Tree Problems

Author

Listed:
  • Vicki Aaronson Hutson

    (Abt Associates, Washington, D.C. 20008)

  • Charles S. ReVelle

    (The Johns Hopkins University, Baltimore, Maryland 21218)

Abstract

Concepts of coverage are extended to a problem of network design. Maximal covering tree problems are introduced to widen the applicability of the minimal spanning tree (MST), a classic network design problem, which defines the minimal length connection of all nodes in a network. Maximal covering tree problems relax the restriction that all nodes must be connected. Instead, maximal covering tree problems identify the best choices for subtrees in the spanning tree network based on the relative benefits and costs of connecting nodes. Two-objective integer programming (IP) models are formulated and solved for the maximal direct covering tree (1) on spanning networks in which arcs currently exist and (2) for the general spanning tree graph.

Suggested Citation

  • Vicki Aaronson Hutson & Charles S. ReVelle, 1989. "Maximal Direct Covering Tree Problems," Transportation Science, INFORMS, vol. 23(4), pages 288-299, November.
    • Handle: RePEc:inm:ortrsc:v:23:y:1989:i:4:p:288-299
    DOI: 10.1287/trsc.23.4.288
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    Cited by:

    1. Timothy J. Niblett & Richard L. Church, 2016. "The Shortest Covering Path Problem," International Regional Science Review, , vol. 39(1), pages 131-151, January.
    2. T. Boffey, 1998. "Efficient solution methods for covering tree problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(2), pages 205-221, December.
    3. Mesa, Juan A. & Brian Boffey, T., 1996. "A review of extensive facility location in networks," European Journal of Operational Research, Elsevier, vol. 95(3), pages 592-603, December.
    4. Moreno Perez, Jose A. & Marcos Moreno-Vega, J. & Rodriguez Martin, Inmaculada, 2003. "Variable neighborhood tabu search and its application to the median cycle problem," European Journal of Operational Research, Elsevier, vol. 151(2), pages 365-378, December.

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