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

A. Karim Abu-Affash; Matthew J. Katz

doi:10.1016/j.ipl.2008.11.009

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 journal › Article › peer-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 language	English
Pages (from-to)	329-333
Number of pages	5
Journal	Information Processing Letters
Volume	109
Issue number	6
DOIs	https://doi.org/10.1016/j.ipl.2008.11.009
State	Published - 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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10.1016/j.ipl.2008.11.009

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title = "Improved bounds on the average distance to the Fermat-Weber center of a convex object",

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].",

keywords = "Approximation algorithms, Computational geometry, Fermat-Weber center",

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T1 - Improved bounds on the average distance to the Fermat-Weber center of a convex object

AU - Abu-Affash, A. Karim

AU - Katz, Matthew J.

PY - 2009/2/28

Y1 - 2009/2/28

N2 - 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].

AB - 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].

KW - Approximation algorithms

KW - Computational geometry

KW - Fermat-Weber center

UR - https://www.scopus.com/pages/publications/58549087531

U2 - 10.1016/j.ipl.2008.11.009

DO - 10.1016/j.ipl.2008.11.009

M3 - Article

AN - SCOPUS:58549087531

SN - 0020-0190

VL - 109

SP - 329

EP - 333

JO - Information Processing Letters

JF - Information Processing Letters

IS - 6

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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