Locating a service facility and a rapid transit line

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

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

3 Citations (Scopus)


In this paper we study a facility location problem in the plane in which a single point (facility) and a rapid transit line (highway) are simultaneously located in order to minimize the total travel time of the clients to the facility, using the L 1 or Manhattan metric. The rapid transit line is represented by a line segment with fixed length and arbitrary orientation. The highway is an alternative transportation system that can be used by the clients to reduce their travel time to the facility. This problem was introduced by Espejo and Rodríguez-Chía in [8]. They gave both a characterization of the optimal solutions and an algorithm running in O(n 3logn) time, where n represents the number of clients. In this paper we show that the Espejo and Rodríguez-Chía's algorithm does not always work correctly. At the same time, we provide a proper characterization of the solutions with a simpler proof and give an algorithm solving the problem in O(n 3) time.

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 pages12
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 distance

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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