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Optimizing some constructions with bars: new geometric knapsack problems

Author

Listed:
  • S. Bereg

    (University of Texas at Dallas)

  • J. M. Díaz-Báñez

    (Universidad de Sevilla)

  • D. Flores-Peñaloza

    (Universidad Nacional Autónoma de México)

  • S. Langerman

    (Université Libre de Bruxelles (ULB))

  • P. Pérez-Lantero

    (Universidad de Valparaíso)

  • J. Urrutia

    (Universidad Nacional Autónoma de México)

Abstract

A set of vertical bars planted on given points of a horizontal line defines a fence composed of the quadrilaterals bounded by successive bars. A set of bars in the plane, each having one endpoint at the origin, defines an umbrella composed of the triangles bounded by successive bars. Given a collection of bars, we study how to use them to build the fence or the umbrella of maximum total area. We present optimal algorithms for these constructions. The problems introduced in this paper are related to the Geometric Knapsack problems (Arkin et al. in Algorithmica 10:399–427, 1993) and the Rearrangement Inequality (Wayne in Scripta Math 12(2):164–169, 1946).

Suggested Citation

  • S. Bereg & J. M. Díaz-Báñez & D. Flores-Peñaloza & S. Langerman & P. Pérez-Lantero & J. Urrutia, 2016. "Optimizing some constructions with bars: new geometric knapsack problems," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1160-1173, April.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:3:d:10.1007_s10878-014-9816-z
    DOI: 10.1007/s10878-014-9816-z
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    References listed on IDEAS

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    1. Richard Church & Charles R. Velle, 1974. "The Maximal Covering Location Problem," Papers in Regional Science, Wiley Blackwell, vol. 32(1), pages 101-118, January.
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