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Maximal covering tree problems

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  • Richard Church
  • John Current

Abstract

Hutson and ReVelle [8] define the maximal direct covering tree problem as a bicriterion problem to identify a subtree of a given tree. The two criteria are to maximize demand covered by the subtree and to minimize the cost of the subtree. Demand at a node on the underlying tree is considered covered if it is within some prespecified covering distance S of the subtree. In the direct covering version of the problem. S = 0. In this article we present a new bicriterion formulation of the maximal direct covering tree problem and present O(n2) algorithms for solving both this problem and the special case where one must add to an existing subtree. The new formulation is extremely concise; consequently, additional constraints may be added where appropriate. This is demonstrated with the addition of a budget constraint. In addition, we demonstrate that the new formulation and algorithm can be readily extended to incorporate indirect covering (i.e., S > 0) as defined by Kim et al. [9]. © 1993 John Wiley & Sons. Inc.

Suggested Citation

  • Richard Church & John Current, 1993. "Maximal covering tree problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 129-142, February.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:1:p:129-142
    DOI: 10.1002/1520-6750(199302)40:13.0.CO;2-T
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    References listed on IDEAS

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    1. Current, J. R. & Re Velle, C. S. & Cohon, J. L., 1985. "The maximum covering/shortest path problem: A multiobjective network design and routing formulation," European Journal of Operational Research, Elsevier, vol. 21(2), pages 189-199, August.
    2. Current, John & Min, HoKey, 1986. "Multiobjective design of transportation networks: Taxonomy and annotation," European Journal of Operational Research, Elsevier, vol. 26(2), pages 187-201, August.
    3. R. K. Ahuja & V. V. S. Murty, 1987. "Exact and Heuristic Algorithms for the Optimum Communication Spanning Tree Problem," Transportation Science, INFORMS, vol. 21(3), pages 163-170, August.
    4. Richard Church & Charles R. Velle, 1974. "The Maximal Covering Location Problem," Papers in Regional Science, Wiley Blackwell, vol. 32(1), pages 101-118, January.
    5. CONSTANTINE TOREGAS & CHARLES ReVELLE, 1972. "Optimal Location Under Time Or Distance Constraints," Papers in Regional Science, Wiley Blackwell, vol. 28(1), pages 133-144, January.
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    1. 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.
    2. 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.

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