Towards the methodology for solving the minimum enclosing ball and related problems

2024/10/14 by Michael N. Vrahatis, Vrahatis, Michael N.
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Aerospace Engineering and Control Systems #Artificial Intelligence (cs.AI) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2410.11063

openalex publication_date 2024/10/14 · openalex created_date 2024/10/20 · openalex updated_date 2026/07/28

Abstract

Methodology is provided towards the solution of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the d-dimensional Euclidean space. Mathematical formulation and typical methods for solving this problem are presented. Also, the paper is focused on areas that are related to this problem, namely: (a) promise problems and property testing, (b) theorems for partitioning and enclosing (covering) a set, and (c) computation of the diameter of a set.

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