, Volume 22, Issue 1, pp 185–207 | Cite as

Locating an axis-parallel rectangle on a Manhattan plane

  • Jack Brimberg
  • Henrik Juel
  • Mark-Christoph Körner
  • Anita Schöbel
Original Paper


In this paper we consider the problem of locating an axis-parallel rectangle in the plane such that the sum of distances between the rectangle and a finite point set is minimized, where the distance is measured by the Manhattan norm 1. In this way we solve an extension of the Weber problem to extensive facility location. As a model, our problem is appropriate for position sensing of rectangular objects.


Weber problem Minisum Dimensional facility Polyhedral norms 

Mathematics Subject Classification (2000)

90B85 97N50 65D10 90C26 



We wish to thank two anonymous referees for their helpful comments. An improved complexity bound on the algorithms given is due to a suggestion by Professor Arie Tamir, and we are also very thankful for that.


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2012

Authors and Affiliations

  • Jack Brimberg
    • 1
  • Henrik Juel
    • 2
  • Mark-Christoph Körner
    • 3
  • Anita Schöbel
    • 3
  1. 1.Royal Military CollegeCanada and Groupe d’Études et de Recherche en Analyse des DécisionsKingstonCanada
  2. 2.Technical University of DenmarkLyngbyDenmark
  3. 3.Georg-August-Universität GöttingenGöttingenGermany

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