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

arXiv: https://arxiv.org/abs/2410.11063 · HTML: https://mlsanity.com/paper/2410.11063/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 105 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Builds on (most cited first, 8 of 8)

- [Theorems of Carath'eodory, Helly, and Tverberg without dimension](https://mlsanity.com/paper/1806.08725/) (2018)
- [Helly-Type Theorems in Property Testing](https://mlsanity.com/paper/1307.8268/) (2013)
- [The discrete yet ubiquitous theorems of Carath'eodory, Helly, Sperner, Tucker, and Tverberg](https://mlsanity.com/paper/1706.05975/) (2017)
- [Testing Distributions of Huge Objects](https://mlsanity.com/paper/2212.12802/) (2022)
- [Generalization of the Apollonius theorem for simplices and related problems](https://mlsanity.com/paper/2401.03232/) (2024)
- [Strongly Sublinear Algorithms for Testing Pattern Freeness](https://mlsanity.com/paper/2106.04856/) (2021)
- [Geometric Covering using Random Fields](https://mlsanity.com/paper/2311.14082/) (2023)
- [Towards the mathematical foundation of the minimum enclosing ball and related problems](https://mlsanity.com/paper/2402.06629/) (2024)

## Abstract (arXiv)

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.