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Optimal Weighted Ancestry Relationships

Author

Listed:
  • Fred Glover

    (University of Colorado)

  • T. Klastorin

    (Wake Forest University)

  • D. Kongman

    (University of Texas)

Abstract

A solution method is given for a class of practical optimization problems requiring the determination of a consistent partial ordering for sets of objects, events, preferences, and the like. These problems are characterized by the existence of "noisy" (or contradictory) links of varying strengths. The origin of this class of problems is an anthropological study in which it is desired to specify a global chronological ordering of ancient cemetery data. A mathematical formulation is given which results in a minimum weight feedback model. A heuristic is developed similar to the Greedy algorithm for minimum weight spanning trees which requires only one pass through the network.

Suggested Citation

  • Fred Glover & T. Klastorin & D. Kongman, 1974. "Optimal Weighted Ancestry Relationships," Management Science, INFORMS, vol. 20(8), pages 1190-1193, April.
    • Handle: RePEc:inm:ormnsc:v:20:y:1974:i:8:p:1190-1193
    DOI: 10.1287/mnsc.20.8.1190
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    File URL: http://dx.doi.org/10.1287/mnsc.20.8.1190
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    Cited by:

    1. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    2. Juan Aparicio & Mercedes Landete & Juan F. Monge, 2020. "A linear ordering problem of sets," Annals of Operations Research, Springer, vol. 288(1), pages 45-64, May.
    3. Javier Alcaraz & Eva M. García-Nové & Mercedes Landete & Juan F. Monge, 2020. "The linear ordering problem with clusters: a new partial ranking," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 646-671, October.
    4. Rafael Martí & Gerhard Reinelt & Abraham Duarte, 2012. "A benchmark library and a comparison of heuristic methods for the linear ordering problem," Computational Optimization and Applications, Springer, vol. 51(3), pages 1297-1317, April.

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