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Bichromatic 2-Center of Pairs of Points

  • Esther M. Arkin
  • José Miguel Díaz-Báñez
  • Ferran Hurtado
  • Piyush Kumar
  • Joseph S. B. Mitchell
  • Belén Palop
  • Pablo Pérez-Lantero
  • Maria Saumell
  • Rodrigo I. Silveira
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7256)

Abstract

We study a class of geometric optimization problems closely related to the 2-center problem: Given a set S of n pairs of points, assign to each point a color (“red” or “blue”) so that each pair’s points are assigned different colors and a function of the radii of the minimum enclosing balls of the red points and the blue points, respectively, is optimized. In particular, we consider the problems of minimizing the maximum and minimizing the sum of the two radii. For each case, minmax and minsum, we consider distances measured in the L 2 and in the L  ∞  metrics. Our problems are motivated by a facility location problem in transportation system design, in which we are given origin/destination pairs of points for desired travel, and our goal is to locate an optimal road/flight segment in order to minimize the travel to/from the endpoints of the segment.

Keywords

Binary Search Facility Location Problem Blue Point Sweep Event Blue Disk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Esther M. Arkin
    • 1
  • José Miguel Díaz-Báñez
    • 2
  • Ferran Hurtado
    • 3
  • Piyush Kumar
    • 4
  • Joseph S. B. Mitchell
    • 1
  • Belén Palop
    • 5
  • Pablo Pérez-Lantero
    • 6
  • Maria Saumell
    • 7
  • Rodrigo I. Silveira
    • 3
  1. 1.Dept. of Appl. Math. and StatisticsState Univ. of NYStony BrookUSA
  2. 2.Departamento Matemática Aplicada IIUniversidad de SevillaSpain
  3. 3.Dept. de Matemàtica Aplicada IIUniversitat Politècnica de CatalunyaSpain
  4. 4.Dept. of Computer ScienceFlorida State UniversityTallahasseeUSA
  5. 5.Departamento de InformáticaUniversidad de ValladolidSpain
  6. 6.Esc. de Ingeniería Civil en InformáticaUniversidad de ValparaísoChile
  7. 7.Dept. of Appl. Math.Charles UniversityPragueCzech Republic

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