Continuous facility location on graphs

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

*Corresponding author for this work

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


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.

Original languageEnglish
Title of host publicationInteger Programming and Combinatorial Optimization - 21st International Conference, IPCO 2020, Proceedings
Subtitle of host publication21st International Conference, IPCO 2020, London, UK, June 8–10, 2020, Proceedings
EditorsDaniel Bienstock, Giacomo Zambelli
Place of PublicationCham
Number of pages11
ISBN (Print)9783030457709
Publication statusPublished - 1 Jan 2020
Event21st Conference on Integer Programming and Combinatorial Optimization: IPCO 2020 - London School of Economics, Virtuell, United Kingdom
Duration: 8 Jun 202010 Jun 2020
Conference number: 21

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12125 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference21st Conference on Integer Programming and Combinatorial Optimization
Abbreviated titleIPCO 2020 LSE
Country/TerritoryUnited Kingdom
Internet address


  • Graph theory
  • Location theory
  • Parametrized complexity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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