Towards the methodology for solving the minimum enclosing ball and related problems
This work addresses a fundamental geometric optimization problem with potential applications in computational geometry and machine learning, but it appears incremental as it builds on existing methods without claiming major breakthroughs.
The paper tackles the minimum enclosing ball problem, which involves finding the smallest sphere that encloses a given set in d-dimensional Euclidean space, and presents a methodology along with related problems such as promise problems, property testing, partitioning theorems, and diameter computation.
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.