Statistics Papers

Document Type

Technical Report

Date of this Version

10-2014

Publication Source

Computational Geometry

Volume

47

Issue

9

Start Page

891

Last Page

898

DOI

10.1016/j.comgeo.2014.04.006

Abstract

Given a set S of n static points and a mobile point p in ℝ2, we study the variations of the smallest circle that encloses S ∪ {p} when p moves along a straight line ℓ. In this work, a complete characterization of the locus of the center of the minimum enclosing circle (MEC) of S ∪ {p}, for p ∈ ℓ, is presented. The locus is a continuous and piecewise differentiable linear function, and each of its differentiable pieces lies either on the edges of the farthest-point Voronoi diagram of S, or on a line segment parallel to the line ℓ. Moreover, the locus has differentiable pieces, which can be computed in linear time, given the farthest-point Voronoi diagram of S.

Copyright/Permission Statement

© 2014 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

farthest-point Voronoi diagram, minimum enclosing circle, mobile facility location

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Date Posted: 25 October 2018

This document has been peer reviewed.