Paper Info
Title
Bounded-Velocity Approximation Of Mobile Euclidean 2-Centres
Abstract
Given a set P of points (clients) in the plane, a Euclidean 2-centre of P is a set of two points (facilities) in the plane such that the maximum distance from any client to its nearest facility is minimized. Geometrically, a Euclidean 2-centre of P corresponds to a cover of P by two discs of minimum radius r (the Euclidean 2-radius). Given a set of mobile clients, where each client follows a continuous trajectory in the plane with bounded velocity, the motion of the corresponding mobile Euclidean 2-centre is not necessarily continuous. Consequently, we consider strategies for defining the trajectories of a pair of mobile facilities that guarantee a fixed-degree approximation of the Euclidean 2-centre while maintaining bounded relative velocity. In an attempt to balance the conflicting goals of closeness of approximation and a low maximum relative velocity, we introduce reflection-based 2-centre functions by reflecting the position of a mobile client across the mobile Steiner centre and the mobile rectilinear 1-centre, respectively.
Year
DOI
Venue
2008
10.1142/S021819590800257X
INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS
Keywords
DocType
Volume
2-centre, motion, approximation, velocity, Euclidean, continuous
Journal
18
Issue
ISSN
Citations 
3
0218-1959
9
PageRank 
References 
Authors
0.65
26
2
Name
Order
Citations
PageRank
Stephane Durocher134242.89
David G. Kirkpatrick22394541.05