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

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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

JEL classifications

  • c02 - Mathematical Methods

Keywords

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

Research Output

A PTAS for the Cluster Editing Problem on Planar Graphs

Berger, A., Grigoriev, A. & Winokurow, A., 7 Jan 2017, Approximation and Online Algorithms. Lecture Notes in Computer Science ed. Springer, Vol. 10138. p. 27-39 (Lecture Notes in Computer Science, Vol. 10138).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Location, pricing and the problem of Apollonius

Berger, A., Grigoriev, A., Panin, A. & Winokurow, A., Dec 2017, In : Optimization Letters. 11, 8, p. 1797–1805 9 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access

Location, Pricing and the Problem of Apollonius

Berger, A., Grigoriev, A., Panin, A. & Winokurow, A., 10 Sep 2016, Discrete Optimization and Operations Research. Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E. A. & Pardalos, P. M. (eds.). Switzerland: Springer, Vol. 9869. p. 563-569 (Lecture Notes in Computer Science, Vol. 9869).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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