Dispersing Obnoxious Facilities on a Graph

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 δ f...

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Bibliographic Details
Published in:Algorithmica Vol. 83; no. 6; pp. 1734 - 1749
Main Authors: Grigoriev, Alexander, Hartmann, Tim A., Lendl, Stefan, Woeginger, Gerhard J.
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2021
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Graph theory
Mathematics of Computing
Operations research
Site selection
Theory of Computation
Facility location
Theory of computation: graph algorithms analysis
Theory of computation: discrete optimization
Algorithms
Mathematics of computing: graph theory
Graph theory
Optimization
Complexity
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary: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 δ from each other. We investigate the complexity of this problem in terms of the rational parameter δ . The problem is polynomially solvable, if the numerator of δ is 1 or 2, while all other cases turn out to be NP-hard.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-021-00800-3