Banik, AritraBhattacharya, Bhaswar BDas, Sandip2023-05-232023-05-232014-10-012018-07-13https://repository.upenn.edu/handle/20.500.14332/48057Given 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.© 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/).farthest-point Voronoi diagramminimum enclosing circlemobile facility locationApplied MathematicsBusinessBusiness AnalyticsManagement Sciences and Quantitative MethodsMathematicsStatistics and ProbabilityReport