Dispersing Obnoxious Facilities on a Graph

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

doi:10.4230/LIPIcs.STACS.2019.33

Dispersing Obnoxious Facilities on a Graph

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

^*Corresponding author for this work

Data Analytics and Digitalisation

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › 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 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 language	English
Title of host publication	36TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2019)
Editors	Rolf Niedermeier, Christophe Paul
Publisher	Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik
Pages	33:1-33:11
Number of pages	11
Volume	126
ISBN (Electronic)	9783959771009
ISBN (Print)	978-3-95977-100-9
DOIs	https://doi.org/10.4230/LIPIcs.STACS.2019.33
Publication status	Published - Mar 2019
Event	International Symposium on Theoretical Aspects of Computer Science - TU Berlin, Berlin, Germany Duration: 13 Mar 2019 → 16 Mar 2019 Conference number: 36 https://stacs2019.akt.tu-berlin.de/

Publication series

Series	Leibniz International Proceedings in Informatics
Volume	126
ISSN	1868-8969

Symposium

Symposium	International Symposium on Theoretical Aspects of Computer Science
Abbreviated title	STACS
Country/Territory	Germany
City	Berlin
Period	13/03/19 → 16/03/19
Internet address	https://stacs2019.akt.tu-berlin.de/

JEL classifications

c63 - "Computational Techniques; Simulation Modeling"
c00 - Mathematical and Quantitative Methods: General

Keywords

Algorithms
Complexity
Facility location
Graph theory
Optimization
algorithms
complexity
optimization
graph theory
facility location

Access to Document

10.4230/LIPIcs.STACS.2019.33

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 (STACS 2019) (Vol. 126, pp. 33:1-33:11). Article 33 Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. https://doi.org/10.4230/LIPIcs.STACS.2019.33

Grigoriev, Alexander ; Hartmann, Tim A. ; Lendl, Stefan et al. / Dispersing Obnoxious Facilities on a Graph. 36TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2019). editor / Rolf Niedermeier ; Christophe Paul. Vol. 126 Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2019. pp. 33:1-33:11 (Leibniz International Proceedings in Informatics, Vol. 126).

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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 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, Facility location, Graph theory, Optimization, 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; International Symposium on Theoretical Aspects of Computer Science, STACS ; Conference date: 13-03-2019 Through 16-03-2019",

year = "2019",

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doi = "10.4230/LIPIcs.STACS.2019.33",

language = "English",

isbn = "978-3-95977-100-9",

volume = "126",

series = "Leibniz International Proceedings in Informatics",

publisher = "Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik",

pages = "33:1--33:11",

editor = "Rolf Niedermeier and Christophe Paul",

booktitle = "36TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2019)",

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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 (STACS 2019). vol. 126, 33, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Leibniz International Proceedings in Informatics, vol. 126, pp. 33:1-33:11, International Symposium on Theoretical Aspects of Computer Science, Berlin, 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 et al.
36TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2019). ed. / Rolf Niedermeier; Christophe Paul. Vol. 126 Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2019. p. 33:1-33:11 33 (Leibniz International Proceedings in Informatics, Vol. 126).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-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 - Conference code: 36

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 - Facility location

KW - Graph theory

KW - Optimization

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 - Leibniz International Proceedings in Informatics

SP - 33:1-33:11

BT - 36TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2019)

A2 - Niedermeier, Rolf

A2 - Paul, Christophe

PB - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik

T2 - International Symposium on Theoretical Aspects of Computer Science

Y2 - 13 March 2019 through 16 March 2019

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 (STACS 2019). Vol. 126. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. 2019. p. 33:1-33:11. 33. (Leibniz International Proceedings in Informatics, Vol. 126). doi: 10.4230/LIPIcs.STACS.2019.33

Dispersing Obnoxious Facilities on a Graph

Abstract

Publication series

Symposium

JEL classifications

Keywords

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