Fast and robust approximation of smallest enclosing balls in arbitrary dimensions
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Given ${\cal A} := \{a^1,\dots,a^m\} \subset \mathbb{R}^n$, we consider the problem of reducing the input set for the computation of the minimum enclosing ball of ${\cal A}$. In this note, given an approximate solution to the minimum enclosing ball problem, we propose a simple procedure to identify and eliminate points in ${\cal A}$ that are guaranteed to lie in the interior of the minimum-radius ball enclosing ${\cal A}$. Our computational results reveal that incorporating this procedure into two recent algorithms proposed by Yıldırım lead to significant speed-ups in running times especially for randomly generated large-scale problems. We also illustrate that the extra overhead due to the elimination procedure remains at an acceptable level for spherical or almost spherical input sets.