The 1-center and 1-highway problem

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)


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 ∈ S d H (p,f), where d H (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(n 2) or O(nlogn) time, depending on whether or not the highway's length is fixed.

Original languageEnglish
Title of host publicationComputational Geometry - XIV Spanish Meeting, EGC 2011, Dedicated to Ferran Hurtado on the Occasion of His 60th Birthday, Revised Selected Papers
Number of pages11
Publication statusPublished - 2012 Nov 30
Externally publishedYes
Event14th Spanish Meeting on Computational Geometry - Alcala de Henares, Spain
Duration: 2011 Jun 272011 Jun 30

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7579 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other14th Spanish Meeting on Computational Geometry
CityAlcala de Henares


  • Facility location
  • Geometric optimization
  • Time metric

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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