EGC 2011: Computational Geometry pp 155-165

# The 1-Center and 1-Highway Problem

• José Miguel Díaz-Báñez
• Matias Korman
• Pablo Pérez-Lantero
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579)

## 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 ∈ Sd 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(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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## Authors and Affiliations

• José Miguel Díaz-Báñez
• 1
• Matias Korman
• 2
• Pablo Pérez-Lantero
• 3