Dispersing Obnoxious Facilities on a Graph

Alexander Grigoriev, Tim A. Hartmann, Stefan Lendl, G.J. Woeginger

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-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 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.
Original languageEnglish
Title of host publication36th International Symposium on Theoretical Aspects of Computer Science
EditorsRolf Niedermeier, Christophe Paul
PublisherSchloss Dagstuhl - Leibniz-Zentrum fuer Informatik
Pages33:1-33:11
Number of pages11
Volume126
ISBN (Print)978-3-95977-100-9
DOIs
Publication statusPublished - Mar 2019
EventInternational Symposium on Theoretical Aspects of Computer Science - TU Berlin, Berlin, Germany
Duration: 13 Mar 201916 Mar 2019
Conference number: 36
https://stacs2019.akt.tu-berlin.de/

Publication series

SeriesLIPIcs
Volume126

Conference

ConferenceInternational Symposium on Theoretical Aspects of Computer Science
Abbreviated titleSTACS
CountryGermany
CityBerlin
Period13/03/1916/03/19
Internet address

Keywords

  • Algorithms
  • Complexity
  • Optimization
  • Graph theory
  • Facility location

Cite this

Grigoriev, A., Hartmann, T. A., Lendl, S., & Woeginger, G. J. (2019). Dispersing Obnoxious Facilities on a Graph. In R. Niedermeier, & C. Paul (Eds.), 36th International Symposium on Theoretical Aspects of Computer Science (Vol. 126, pp. 33:1-33:11). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. LIPIcs, Vol.. 126 https://doi.org/10.4230/LIPIcs.STACS.2019.33
Grigoriev, Alexander ; Hartmann, Tim A. ; Lendl, Stefan ; Woeginger, G.J. / Dispersing Obnoxious Facilities on a Graph. 36th International Symposium on Theoretical Aspects of Computer Science. editor / Rolf Niedermeier ; Christophe Paul. Vol. 126 Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2019. pp. 33:1-33:11 (LIPIcs, Vol. 126).
@inproceedings{4e7b6c66c4124a1b94ac9697484ca9d3,
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 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.",
keywords = "Algorithms, Complexity, Optimization, Graph theory, Facility location",
author = "Alexander Grigoriev and Hartmann, {Tim A.} and Stefan Lendl and G.J. Woeginger",
note = "data source: NO DATA USED",
year = "2019",
month = "3",
doi = "10.4230/LIPIcs.STACS.2019.33",
language = "English",
isbn = "978-3-95977-100-9",
volume = "126",
series = "LIPIcs",
pages = "33:1--33:11",
editor = "Rolf Niedermeier and Christophe Paul",
booktitle = "36th International Symposium on Theoretical Aspects of Computer Science",
publisher = "Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik",
address = "Germany",

}

Grigoriev, A, Hartmann, TA, Lendl, S & Woeginger, GJ 2019, Dispersing Obnoxious Facilities on a Graph. in R Niedermeier & C Paul (eds), 36th International Symposium on Theoretical Aspects of Computer Science. vol. 126, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, LIPIcs, vol. 126, pp. 33:1-33:11, International Symposium on Theoretical Aspects of Computer Science, Berlin, Germany, 13/03/19. https://doi.org/10.4230/LIPIcs.STACS.2019.33

Dispersing Obnoxious Facilities on a Graph. / Grigoriev, Alexander; Hartmann, Tim A. ; Lendl, Stefan ; Woeginger, G.J.

36th International Symposium on Theoretical Aspects of Computer Science. ed. / Rolf Niedermeier; Christophe Paul. Vol. 126 Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2019. p. 33:1-33:11 (LIPIcs, Vol. 126).

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

TY - GEN

T1 - Dispersing Obnoxious Facilities on a Graph

AU - Grigoriev, Alexander

AU - Hartmann, Tim A.

AU - Lendl, Stefan

AU - Woeginger, G.J.

N1 - data source: NO DATA USED

PY - 2019/3

Y1 - 2019/3

N2 - 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.

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 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.

KW - Algorithms

KW - Complexity

KW - Optimization

KW - Graph theory

KW - Facility location

U2 - 10.4230/LIPIcs.STACS.2019.33

DO - 10.4230/LIPIcs.STACS.2019.33

M3 - Conference article in proceeding

SN - 978-3-95977-100-9

VL - 126

T3 - LIPIcs

SP - 33:1-33:11

BT - 36th International Symposium on Theoretical Aspects of Computer Science

A2 - Niedermeier, Rolf

A2 - Paul, Christophe

PB - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik

ER -

Grigoriev A, Hartmann TA, Lendl S, Woeginger GJ. Dispersing Obnoxious Facilities on a Graph. In Niedermeier R, Paul C, editors, 36th International Symposium on Theoretical Aspects of Computer Science. Vol. 126. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. 2019. p. 33:1-33:11. (LIPIcs, Vol. 126). https://doi.org/10.4230/LIPIcs.STACS.2019.33