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.
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Díaz-Báñez, J.M., Korman, M., Pérez-Lantero, P., Ventura, I. (2012). The 1-Center and 1-Highway Problem. In: Márquez, A., Ramos, P., Urrutia, J. (eds) Computational Geometry. EGC 2011. Lecture Notes in Computer Science, vol 7579. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34191-5_15
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