Improved bounds on the average distance to the Fermat-Weber center of a convex object

A. Karim Abu-Affash, Matthew J. Katz

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We show that for any convex object Q in the plane, the average distance between the Fermat-Weber center of Q and the points in Q is at least 4 Δ (Q) / 25, and at most 2 Δ (Q) / (3 sqrt(3)), where Δ (Q) is the diameter of Q. We use the former bound to improve the approximation ratio of a load-balancing algorithm of Aronov et al. [B. Aronov, P. Carmi, M.J. Katz, Minimum-cost load-balancing partitions, Algorithmica, in press].

Original languageEnglish
Pages (from-to)329-333
Number of pages5
JournalInformation Processing Letters
Volume109
Issue number6
DOIs
StatePublished - 28 Feb 2009

Keywords

  • Approximation algorithms
  • Computational geometry
  • Fermat-Weber center

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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