Locating an axis-parallel rectangle on a Manhattan plane

• Jack Brimberg ^[3] ; Henrik Juel ^[1] ; Mark-Christoph Körner ^[2] ; Anita Schöbel ^[2]
  1. [1] Technical University of Denmark

     Technical University of Denmark

     Dinamarca

     
  2. [2] University of Göttingen

     University of Göttingen

     Landkreis Göttingen, Alemania

     
  3. [3] Royal Military College, Canadá

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• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 22, Nº. 1, 2014, págs. 185-207
• Idioma: inglés
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• Resumen

  • 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 ℓ 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.