Continuous facility location on graphs

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

doi:10.1007/978-3-030-45771-6_14

Continuous facility location on graphs

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

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Diskrete Mathematik (5050)

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Begutachtung

Abstract

We study a continuous facility location problem on undirected graphs where all edges have unit length and where the facilities may be positioned at the vertices as well as at interior points of the edges. The goal is to cover the entire graph with a minimum number of facilities with covering range δ > 0. In other words, we want to position as few facilities as possible subject to the condition that every point on every edge is at distance at most δ from one of these facilities. We investigate this covering problem in terms of the rational parameter δ. We prove that the problem is polynomially solvable whenever δ is a unit fraction, and that the problem is NP-hard for all non unit fractions δ. We also analyze the parametrized complexity with the solution size as parameter: The resulting problem is fixed parameter tractable for all δ < 3/2, and it is W[2]-hard for all δ ≥ 3/2.

Originalsprache	englisch
Titel	Integer Programming and Combinatorial Optimization - 21st International Conference, IPCO 2020, Proceedings
Untertitel	21st International Conference, IPCO 2020, London, UK, June 8–10, 2020, Proceedings
Redakteure/-innen	Daniel Bienstock, Giacomo Zambelli
Erscheinungsort	Cham
Herausgeber (Verlag)	Springer
Seiten	171-181
Seitenumfang	11
ISBN (Print)	9783030457709
DOIs	https://doi.org/10.1007/978-3-030-45771-6_14
Publikationsstatus	Veröffentlicht - 1 Jan. 2020
Veranstaltung	21st Conference on Integer Programming and Combinatorial Optimization: IPCO 2020 - London School of Economics, Virtuell, Großbritannien / Vereinigtes Königreich Dauer: 8 Juni 2020 → 10 Juni 2020 Konferenznummer: 21 http://www.lse.ac.uk/IPCO-2020

Publikationsreihe

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Band	12125 LNCS
ISSN (Print)	0302-9743
ISSN (elektronisch)	1611-3349

Konferenz

Konferenz	21st Conference on Integer Programming and Combinatorial Optimization
Kurztitel	IPCO 2020 LSE
Land/Gebiet	Großbritannien / Vereinigtes Königreich
Ort	Virtuell
Zeitraum	8/06/20 → 10/06/20
Internetadresse	http://www.lse.ac.uk/IPCO-2020

ASJC Scopus subject areas

Theoretische Informatik
Informatik (insg.)

Zugriff auf Dokument

10.1007/978-3-030-45771-6_14

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http://www.scopus.com/inward/record.url?scp=85083993456&partnerID=8YFLogxK

Dieses zitieren

Hartmann, T. A., Lendl, S., & Woeginger, G. J. (2020). Continuous facility location on graphs. in D. Bienstock, & G. Zambelli (Hrsg.), Integer Programming and Combinatorial Optimization - 21st International Conference, IPCO 2020, Proceedings: 21st International Conference, IPCO 2020, London, UK, June 8–10, 2020, Proceedings (S. 171-181). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Band 12125 LNCS). Springer. https://doi.org/10.1007/978-3-030-45771-6_14

Continuous facility location on graphs. / Hartmann, Tim A.; Lendl, Stefan; Woeginger, Gerhard J.
Integer Programming and Combinatorial Optimization - 21st International Conference, IPCO 2020, Proceedings: 21st International Conference, IPCO 2020, London, UK, June 8–10, 2020, Proceedings. Hrsg. / Daniel Bienstock; Giacomo Zambelli. Cham: Springer, 2020. S. 171-181 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Band 12125 LNCS).

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Begutachtung

Hartmann, TA, Lendl, S & Woeginger, GJ 2020, Continuous facility location on graphs. in D Bienstock & G Zambelli (Hrsg.), Integer Programming and Combinatorial Optimization - 21st International Conference, IPCO 2020, Proceedings: 21st International Conference, IPCO 2020, London, UK, June 8–10, 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bd. 12125 LNCS, Springer, Cham, S. 171-181, 21st Conference on Integer Programming and Combinatorial Optimization, Virtuell, Großbritannien / Vereinigtes Königreich, 8/06/20. https://doi.org/10.1007/978-3-030-45771-6_14

Hartmann TA, Lendl S, Woeginger GJ. Continuous facility location on graphs. in Bienstock D, Zambelli G, Hrsg., Integer Programming and Combinatorial Optimization - 21st International Conference, IPCO 2020, Proceedings: 21st International Conference, IPCO 2020, London, UK, June 8–10, 2020, Proceedings. Cham: Springer. 2020. S. 171-181. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-45771-6_14

Hartmann, Tim A. ; Lendl, Stefan ; Woeginger, Gerhard J. / Continuous facility location on graphs. Integer Programming and Combinatorial Optimization - 21st International Conference, IPCO 2020, Proceedings: 21st International Conference, IPCO 2020, London, UK, June 8–10, 2020, Proceedings. Hrsg. / Daniel Bienstock ; Giacomo Zambelli. Cham : Springer, 2020. S. 171-181 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Continuous facility location on graphs",

abstract = "We study a continuous facility location problem on undirected graphs where all edges have unit length and where the facilities may be positioned at the vertices as well as at interior points of the edges. The goal is to cover the entire graph with a minimum number of facilities with covering range δ > 0. In other words, we want to position as few facilities as possible subject to the condition that every point on every edge is at distance at most δ from one of these facilities. We investigate this covering problem in terms of the rational parameter δ. We prove that the problem is polynomially solvable whenever δ is a unit fraction, and that the problem is NP-hard for all non unit fractions δ. We also analyze the parametrized complexity with the solution size as parameter: The resulting problem is fixed parameter tractable for all δ < 3/2, and it is W[2]-hard for all δ ≥ 3/2.",

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author = "Hartmann, {Tim A.} and Stefan Lendl and Woeginger, {Gerhard J.}",

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doi = "10.1007/978-3-030-45771-6_14",

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note = "21st Conference on Integer Programming and Combinatorial Optimization : IPCO 2020, IPCO 2020 LSE ; Conference date: 08-06-2020 Through 10-06-2020",

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AU - Hartmann, Tim A.

AU - Lendl, Stefan

AU - Woeginger, Gerhard J.

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PY - 2020/1/1

Y1 - 2020/1/1

N2 - We study a continuous facility location problem on undirected graphs where all edges have unit length and where the facilities may be positioned at the vertices as well as at interior points of the edges. The goal is to cover the entire graph with a minimum number of facilities with covering range δ > 0. In other words, we want to position as few facilities as possible subject to the condition that every point on every edge is at distance at most δ from one of these facilities. We investigate this covering problem in terms of the rational parameter δ. We prove that the problem is polynomially solvable whenever δ is a unit fraction, and that the problem is NP-hard for all non unit fractions δ. We also analyze the parametrized complexity with the solution size as parameter: The resulting problem is fixed parameter tractable for all δ < 3/2, and it is W[2]-hard for all δ ≥ 3/2.

AB - We study a continuous facility location problem on undirected graphs where all edges have unit length and where the facilities may be positioned at the vertices as well as at interior points of the edges. The goal is to cover the entire graph with a minimum number of facilities with covering range δ > 0. In other words, we want to position as few facilities as possible subject to the condition that every point on every edge is at distance at most δ from one of these facilities. We investigate this covering problem in terms of the rational parameter δ. We prove that the problem is polynomially solvable whenever δ is a unit fraction, and that the problem is NP-hard for all non unit fractions δ. We also analyze the parametrized complexity with the solution size as parameter: The resulting problem is fixed parameter tractable for all δ < 3/2, and it is W[2]-hard for all δ ≥ 3/2.

KW - Graph theory

KW - Location theory

KW - Parametrized complexity

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DO - 10.1007/978-3-030-45771-6_14

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BT - Integer Programming and Combinatorial Optimization - 21st International Conference, IPCO 2020, Proceedings

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ER -

Continuous facility location on graphs

Abstract

Publikationsreihe

Konferenz

ASJC Scopus subject areas

Zugriff auf Dokument

Andere Dateien und Links

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