Computational Geometry pp 155-165

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579) | Cite as

The 1-Center and 1-Highway Problem

  • José Miguel Díaz-Báñez
  • Matias Korman
  • Pablo Pérez-Lantero
  • Inmaculada Ventura

Abstract

In this paper we extend the Rectilinear 1-center as follows: Given a set S of n points in the plane, we are interested in locating a facility point f and a rapid transit line (highway) H that together minimize the expression max p ∈ SdH(p,f), where dH(p,f) is the travel time between p and f. A point p ∈ S uses H to reach f if H saves time for p. We solve the problem in O(n2) or O(nlogn) time, depending on whether or not the highway’s length is fixed.

Keywords

Geometric optimization Facility location Time metric 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • José Miguel Díaz-Báñez
    • 1
  • Matias Korman
    • 2
  • Pablo Pérez-Lantero
    • 3
  • Inmaculada Ventura
    • 1
  1. 1.Departamento de Matemática Aplicada IIUniversidad de SevillaSpain
  2. 2.Universitat Politècnica de Catalunya (UPC)BarcelonaSpain
  3. 3.Escuela de Ingeniería Civil en InformáticaUniversidad de ValparaísoChile

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