A fast algorithm for the alpha-connected two-center decision problem

Huang, Po-Hsueh; Tsai, Yin Te; Tang, Chuan Yi

doi:10.1016/s0020-0190(02)00402-7

Cited by 10 publications

(7 citation statements)

References 15 publications

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“…For any real number r > 0, let Center(T, r) be the locus of the centers of the axis-parallel squares of radius r (i.e., L ∞ balls) that cover T . A similar definition can be seen in [12]. Lemma 2.…”

Section: Locating a Turnpikementioning

confidence: 89%

The 1-Center and 1-Highway Problem

Díaz-Báñez

Korman

Pérez-Lantero

et al. 2012

Lecture Notes in Computer Science

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Abstract. We study a variation of the 1-center problem in which, in addition to a single supply facility, we are allowed to locate a highway. This highway increases the transportation speed between any demand point and the facility. That is, given a set S of points and v > 1, we are interested in locating the facility point f and the highway h that minimize the expression maxp∈S d h (p, f ), where d h is the time needed to travel between p and f . We consider two types of highways (freeways and turnpikes) and study the cases in which the highway's length is fixed by the user (or can be modified to further decrease the transportation time).

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Section: Locating a Turnpikementioning

confidence: 89%

The 1-Center and 1-Highway Problem

Díaz-Báñez

Korman

Pérez-Lantero

et al. 2012

Lecture Notes in Computer Science

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“…On the contrary, a polygonal p -center is a nonconvex optimization problem. Therefore, it still remains a challenge to find the global optimal solution [22,23].…”

Section: Voronoi Diagrammentioning

confidence: 99%

Rapidly converging solution for p-centers in nonconvex regions

Mangla¹,

Garg²

2017

Turk J Elec Eng & Comp Sci

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This paper aims to locate p resources in a nonconvex demand plane having n demand points. The objective of the location problem is to find the location for these p resources so that the distance from each of n demand points to its nearest resource is minimized, thus simulating a p -center problem. We employ various geometrical structures for solving this location problem. The suggested approach is also capable of finding the optimal value of p so that all demand points have at least one resource at a distance ∆ , where ∆ is the maximum permissible distance for emergency services.Finally, an implementation of the proposed approach is presented and it is observed that the suggested approach rapidly converges towards the optimal location.

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“…For any r ≥ 0, let Center(P, r ) be the locus of the points u such that P ⊆ B(u, r ), that is, Center(P, r ) = p∈P B( p, r ). A similar definition has been used by Huang et al (2003).…”

Section: Lemma 1 For Any Set S Of N Points An Optimal Partitionmentioning

confidence: 99%

The 1-Center and 1-Highway problem revisited

et al. 2015

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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∈S T h ( p, f ), where T h ( 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 L 1 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(n 2 ) or O(n log 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(n log n) time.A preliminary version of this research appeared in the XIV Spanish Meeting on Computational Geometry (Díaz-Báñez et al. 2011).

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A fast algorithm for the alpha-connected two-center decision problem

Cited by 10 publications

References 15 publications

The 1-Center and 1-Highway Problem

The 1-Center and 1-Highway Problem

Rapidly converging solution for p-centers in nonconvex regions

The 1-Center and 1-Highway problem revisited

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