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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.
CitationDíaz, J. [et al.]. The 1-Center and 1-Highway Problem. A: Spanish Meeting on Computational Geometry. "Computational Geometry: XIV Spanish Meeting on Computational Geometry, EGC 2011, dedicated to Ferran Hurtado on the occasion of His 60th birthday, Alcalá de Henares, Spain, June 27-30, 2011: revised selected papers". Alcalá de Henares (Madrid): Springer, 2011, p. 155-165.
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