Dispersing Obnoxious Facilities on a Graph

Alexander Grigoriev; Tim A.  Hartmann; Stefan  Lendl; Gerhard J. Woeginger

doi:10.1007/s00453-021-00800-3

Dispersing Obnoxious Facilities on a Graph

Alexander Grigoriev, Tim A. Hartmann, Stefan Lendl, Gerhard J. Woeginger^*

^*Corresponding author for this work

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

Abstract

We study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance delta from each other. We investigate the complexity of this problem in terms of the rational parameter delta. The problem is polynomially solvable, if the numerator of delta is 1 or 2, while all other cases turn out to be NP-hard.

Original language	English
Pages (from-to)	1734-1749
Number of pages	16
Journal	Algorithmica
Volume	83
Issue number	6
DOIs	https://doi.org/10.1007/s00453-021-00800-3
Publication status	Published - Jun 2021

JEL classifications

c00 - Mathematical and Quantitative Methods: General
c02 - Mathematical Methods

Keywords

Algorithms
Facility location
Complexity
Optimization
Graph theory

Access to Document

10.1007/s00453-021-00800-3Licence: CC BY

https://link.springer.com/article/10.1007/s00453-021-00800-3Licence: CC BY

Cite this

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title = "Dispersing Obnoxious Facilities on a Graph",

abstract = "We study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance delta from each other. We investigate the complexity of this problem in terms of the rational parameter delta. The problem is polynomially solvable, if the numerator of delta is 1 or 2, while all other cases turn out to be NP-hard.",

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AB - We study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance delta from each other. We investigate the complexity of this problem in terms of the rational parameter delta. The problem is polynomially solvable, if the numerator of delta is 1 or 2, while all other cases turn out to be NP-hard.

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KW - Facility location

KW - Complexity

KW - Optimization

KW - Graph theory

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