On linear-time deterministic algorithms for optimization problems in fixed dimension
Journal of Algorithms
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Mobile facility location (extended abstract)
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
An Efficient Multi-Dimensional Searching Technique and itsApplications
An Efficient Multi-Dimensional Searching Technique and itsApplications
Competitive algorithms for maintaining a mobile center
Mobile Networks and Applications
Geometric facility location under continuous motion: bounded-velocity approximations to the mobile euclidean k-centre and k-median problems
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In this paper we study the variations in the center and the radius of the minimum enclosing circle (MEC) of a set of fixed points and one mobile point, moving along a straight line l. Given a set S of n points and a line l in R2, we completely characterize the locus of the center of MECof the set S∪{p}, for all p ∈ l. We show that the locus is a continuous and piecewise differentiable linear function, and each of its differentiable piece lies either on the edges of the farthest-point Voronoi diagram of S, or on a line segment parallel to the line l. Moreover, we prove that the locus can have at most O(n) differentiable pieces and can be computed in linear time, given the farthest-point Voronoi diagram of S.