An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions

Andre Berger; Alexander Grigoriev; Andrej Winokurow

doi:10.1007/s10589-017-9935-4

An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions

Andre Berger, Alexander Grigoriev^*, Andrej Winokurow

^*Corresponding author for this work

QE Operations research

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

The single facility location problem with demand regions seeks for a facility location minimizing the sum of the distances from n demand regions to the facility. The demand regions represent sales markets where the transportation costs are negligible. In this paper, we assume that all demand regions are disks of the same radius, and the distances are measured by a rectilinear norm, e.g. ℓ ₁ or ℓ _∞. We develop an exact combinatorial algorithm running in time O(nlog ^cn) for some c dependent only on the space dimension. The algorithm is generalizable to the other polyhedral norms.

Original language	English
Pages (from-to)	661–669
Number of pages	9
Journal	Computational Optimization and Applications
Volume	68
Issue number	3
DOIs	https://doi.org/10.1007/s10589-017-9935-4
Publication status	Published - 1 Dec 2017

JEL classifications

c02 - Mathematical Methods

Keywords

Polyhedral norm
Exact algorithm
Single facility location proble
1-median
Rectilinear norm
Polyhedral norm
Single facility location problem
ORDERED MEDIAN PROBLEMS

Access to Document

10.1007/s10589-017-9935-4Licence: CC BY

2 Chapter
1 Article

A PTAS for the Cluster Editing Problem on Planar Graphs
Berger, A., Grigoriev, A. & Winokurow, A., 7 Jan 2017, Approximation and Online Algorithms. Lecture Notes in Computer Science ed. Springer, Vol. 10138. p. 27-39 (Lecture Notes in Computer Science, Vol. 10138).
Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic
Location, pricing and the problem of Apollonius
Berger, A., Grigoriev, A., Panin, A. & Winokurow, A., Dec 2017, In: Optimization Letters. 11, 8, p. 1797–1805 9 p.
Research output: Contribution to journal › Article › Academic › peer-review

Open Access
Location, Pricing and the Problem of Apollonius
Berger, A., Grigoriev, A., Panin, A. & Winokurow, A., 10 Sept 2016, Discrete Optimization and Operations Research. Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E. A. & Pardalos, P. M. (eds.). Switzerland: Springer, Vol. 9869. p. 563-569 (Lecture Notes in Computer Science, Vol. 9869).
Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

Cite this

@article{3ace50b50bcb4139a8fdc0bbd5196595,

title = "An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions",

abstract = "The single facility location problem with demand regions seeks for a facility location minimizing the sum of the distances from n demand regions to the facility. The demand regions represent sales markets where the transportation costs are negligible. In this paper, we assume that all demand regions are disks of the same radius, and the distances are measured by a rectilinear norm, e.g. ℓ 1 or ℓ ∞. We develop an exact combinatorial algorithm running in time O(nlog cn) for some c dependent only on the space dimension. The algorithm is generalizable to the other polyhedral norms.",

keywords = "Polyhedral norm , Exact algorithm, Single facility location proble, 1-median, Rectilinear norm, Polyhedral norm, Single facility location problem, ORDERED MEDIAN PROBLEMS",

author = "Andre Berger and Alexander Grigoriev and Andrej Winokurow",

note = "NO DATA USED",

year = "2017",

month = dec,

day = "1",

doi = "10.1007/s10589-017-9935-4",

language = "English",

volume = "68",

pages = "661–669",

journal = "Computational Optimization and Applications",

issn = "0926-6003",

publisher = "Springer",

number = "3",

}

TY - JOUR

T1 - An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions

AU - Berger, Andre

AU - Grigoriev, Alexander

AU - Winokurow, Andrej

N1 - NO DATA USED

PY - 2017/12/1

Y1 - 2017/12/1

N2 - The single facility location problem with demand regions seeks for a facility location minimizing the sum of the distances from n demand regions to the facility. The demand regions represent sales markets where the transportation costs are negligible. In this paper, we assume that all demand regions are disks of the same radius, and the distances are measured by a rectilinear norm, e.g. ℓ 1 or ℓ ∞. We develop an exact combinatorial algorithm running in time O(nlog cn) for some c dependent only on the space dimension. The algorithm is generalizable to the other polyhedral norms.

AB - The single facility location problem with demand regions seeks for a facility location minimizing the sum of the distances from n demand regions to the facility. The demand regions represent sales markets where the transportation costs are negligible. In this paper, we assume that all demand regions are disks of the same radius, and the distances are measured by a rectilinear norm, e.g. ℓ 1 or ℓ ∞. We develop an exact combinatorial algorithm running in time O(nlog cn) for some c dependent only on the space dimension. The algorithm is generalizable to the other polyhedral norms.

KW - Polyhedral norm

KW - Exact algorithm

KW - Single facility location proble

KW - 1-median

KW - Rectilinear norm

KW - Polyhedral norm

KW - Single facility location problem

KW - ORDERED MEDIAN PROBLEMS

U2 - 10.1007/s10589-017-9935-4

DO - 10.1007/s10589-017-9935-4

M3 - Article

SN - 0926-6003

VL - 68

SP - 661

EP - 669

JO - Computational Optimization and Applications

JF - Computational Optimization and Applications

IS - 3

ER -

An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions

Abstract

JEL classifications

Keywords

Access to Document

Fingerprint

Research output

A PTAS for the Cluster Editing Problem on Planar Graphs

Location, pricing and the problem of Apollonius

Location, Pricing and the Problem of Apollonius

Cite this