Improved bounds on the average distance to the fermat-weber center of a convex object

A. Karim Abu-Affash; Matthew J. Katz

Improved bounds on the average distance to the fermat-weber center of a convex object

A. Karim Abu-Affash, Matthew J. Katz

Department of Computer Science

Research output: Contribution to conference › Paper › peer-review

2 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 4Δ(Q)/25, and at most 2Δ(Q)/(3√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. [1].

Original language	English
Pages	147-150
Number of pages	4
State	Published - 1 Dec 2008
Event	20th Annual Canadian Conference on Computational Geometry, CCCG 2008 - Montreal, QC, Canada Duration: 13 Aug 2008 → 15 Aug 2008

Conference

Conference	20th Annual Canadian Conference on Computational Geometry, CCCG 2008
Country/Territory	Canada
City	Montreal, QC
Period	13/08/08 → 15/08/08

ASJC Scopus subject areas

Geometry and Topology

Cite this

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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 4Δ(Q)/25, and at most 2Δ(Q)/(3√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. [1].",

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year = "2008",

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pages = "147--150",

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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 - 2008/12/1

Y1 - 2008/12/1

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 4Δ(Q)/25, and at most 2Δ(Q)/(3√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. [1].

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 4Δ(Q)/25, and at most 2Δ(Q)/(3√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. [1].

UR - http://www.scopus.com/inward/record.url?scp=84893368637&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:84893368637

SP - 147

EP - 150

T2 - 20th Annual Canadian Conference on Computational Geometry, CCCG 2008

Y2 - 13 August 2008 through 15 August 2008

ER -

Improved bounds on the average distance to the fermat-weber center of a convex object

Abstract

Conference

ASJC Scopus subject areas

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