Dispersing Obnoxious Facilities on a Graph

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

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Author Details

Alexander Grigoriev
  • Department of Quantitative Economics, Maastricht University, Maastricht, The Netherlands
Tim A. Hartmann
  • Department of Computer Science, RWTH Aachen, Aachen, Germany
Stefan Lendl
  • Institute of Discrete Mathematics, TU Graz, Graz Austria
Gerhard J. Woeginger
  • Department of Computer Science, RWTH Aachen, Aachen Germany


The research in this paper has been started during the Lorentz Center Workshop on Fixed-Parameter Computational Geometry, which was organized in May 2018 in Leiden. We thank the Lorentz Center for its hospitality. Alexander Grigoriev and Gerhard Woeginger acknowledge helpful discussions with Fedor Fomin, Petr Golovach and Jesper Nederlof.

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Alexander Grigoriev, Tim A. Hartmann, Stefan Lendl, and Gerhard J. Woeginger. Dispersing Obnoxious Facilities on a Graph. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 33:1-33:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Discrete optimization
  • algorithms
  • complexity
  • optimization
  • graph theory
  • facility location


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