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

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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
Volume68
Issue number3
DOIs
Publication statusPublished - Dec 2017

Keywords

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

Cite this

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title = "An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions",
abstract = "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.",
keywords = "Polyhedral norm , Exact algorithm, Single facility location proble, 1-median, Rectilinear norm, Polyhedral norm, Single facility location problem, ORDERED MEDIAN PROBLEMS",
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An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions. / Berger, Andre; Grigoriev, Alexander; Winokurow, Andrej.

In: Computational Optimization and Applications, Vol. 68, No. 3, 12.2017, p. 661–669.

Research output: Contribution to journalArticleAcademicpeer-review

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KW - ORDERED MEDIAN PROBLEMS

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