TY - JOUR

T1 - The 1-Center and 1-Highway problem revisited

AU - Díaz-Báñez, J. M.

AU - Korman, M.

AU - Pérez-Lantero, P.

AU - Ventura, I.

N1 - Funding Information:
J. M. Díaz-Báñez, P. Pérez-Lantero and I. Ventura were partially supported by the project FEDER MEC MTM2009-08652. J. M. Díaz-Báñez, M. Korman and I. Ventura were partially supported by ESF EUROCORES programme EuroGIGA, CRP ComPoSe: grant EUI-EURC-2011-4306. M. Korman was partially supported by the Secretary for Universities and Research of the Ministry of Economy and Knowledge of the Government of Catalonia and the European Union. P. Pérez-Lantero was partially supported by project Millennium Nucleus Information and Coordination in Networks ICM/FIC RC130003 (Chile).
Publisher Copyright:
© 2015, Springer Science+Business Media New York.

PY - 2016/11/1

Y1 - 2016/11/1

N2 - In this paper we extend the Rectilinear 1-center problem as follows: given a set S of n demand points in the plane, simultaneously locate a facility point f and a rapid transit line (i.e. highway) h that together minimize the expression max p∈STh(p, f) , where Th(p, f) denotes the travel time between p and f. A point of S uses h to reach f if h saves time: every point p∈ S moves outside h at unit speed under the L1 metric, and moves along h at a given speed v> 1. We consider two types of highways: (1) a turnpike in which the demand points can enter/exit the highway only at the endpoints; and (2) a freeway problem in which the demand points can enter/exit the highway at any point. We solve the location problem for the turnpike case in O(n2) or O(nlog n) time, depending on whether or not the highway’s length is fixed. In the freeway case, independently of whether the highway’s length is fixed or not, the location problem can be solved in O(nlog n) time.

AB - In this paper we extend the Rectilinear 1-center problem as follows: given a set S of n demand points in the plane, simultaneously locate a facility point f and a rapid transit line (i.e. highway) h that together minimize the expression max p∈STh(p, f) , where Th(p, f) denotes the travel time between p and f. A point of S uses h to reach f if h saves time: every point p∈ S moves outside h at unit speed under the L1 metric, and moves along h at a given speed v> 1. We consider two types of highways: (1) a turnpike in which the demand points can enter/exit the highway only at the endpoints; and (2) a freeway problem in which the demand points can enter/exit the highway at any point. We solve the location problem for the turnpike case in O(n2) or O(nlog n) time, depending on whether or not the highway’s length is fixed. In the freeway case, independently of whether the highway’s length is fixed or not, the location problem can be solved in O(nlog n) time.

KW - Facility location

KW - Geometric optimization

KW - Rectilinear 1-center problem

KW - Time metric

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U2 - 10.1007/s10479-015-1790-z

DO - 10.1007/s10479-015-1790-z

M3 - Article

AN - SCOPUS:84921894173

SN - 0254-5330

VL - 246

SP - 167

EP - 179

JO - Annals of Operations Research

JF - Annals of Operations Research

IS - 1-2

ER -