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The location of median paths on grid graphs

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  • Ronald Becker
  • Isabella Lari
  • Andrea Scozzari
  • Giovanni Storchi

Abstract

In this paper we consider the location of a path shaped facility on a grid graph. In the literature this problem was extensively studied on particular classes of graphs as trees or series-parallel graphs. We consider here the problem of finding a path which minimizes the sum of the (shortest) distances from it to the other vertices of the grid, where the path is also subject to an additional constraint that takes the form either of the length of the path or of the cardinality. We study the complexity of these problems and we find two polynomial time algorithms for two special cases, with time complexity of O(n) and O(nℓ) respectively, where n is the number of vertices of the grid and ℓ is the cardinality of the path to be located. The literature about locating dimensional facilities distinguishes between the location of extensive facilities in continuous spaces and network facility location. We will show that the problems presented here have a close connection with continuous dimensional facility problems, so that the procedures provided can also be useful for solving some open problems of dimensional facilities location in the continuous case. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Ronald Becker & Isabella Lari & Andrea Scozzari & Giovanni Storchi, 2007. "The location of median paths on grid graphs," Annals of Operations Research, Springer, vol. 150(1), pages 65-78, March.
    • Handle: RePEc:spr:annopr:v:150:y:2007:i:1:p:65-78:10.1007/s10479-006-0162-0
    DOI: 10.1007/s10479-006-0162-0
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    References listed on IDEAS

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    1. Diaz-Banez, J. M. & Mesa, J. A., 2001. "Fitting rectilinear polygonal curves to a set of points in the plane," European Journal of Operational Research, Elsevier, vol. 130(1), pages 214-222, April.
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    Cited by:

    1. Justo Puerto & Federica Ricca & Andrea Scozzari, 2018. "Extensive facility location problems on networks: an updated review," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 187-226, July.
    2. Lari, Isabella & Ricca, Federica & Scozzari, Andrea, 2008. "Comparing different metaheuristic approaches for the median path problem with bounded length," European Journal of Operational Research, Elsevier, vol. 190(3), pages 587-597, November.

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