An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions

Andre Berger, Alexander Grigoriev*, Andrej Winokurow

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


The single facility location problem with demand regions seeks for a facility location minimizing the sum of the distances from n demand regions to the facility. The demand regions represent sales markets where the transportation costs are negligible. In this paper, we assume that all demand regions are disks of the same radius, and the distances are measured by a rectilinear norm, e.g. ℓ1 or ℓ∞ . We develop an exact combinatorial algorithm running in time O(nlog^c n) for some c dependent only on the space dimension. The algorithm is generalizable to the other polyhedral norms.
Original languageEnglish
Pages (from-to)661–669
Number of pages9
JournalComputational Optimization and Applications
Issue number3
Publication statusPublished - Dec 2017

JEL classifications

  • c02 - Mathematical Methods


  • Polyhedral norm
  • Exact algorithm
  • Single facility location proble
  • 1-median
  • Rectilinear norm
  • Polyhedral norm
  • Single facility location problem

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