# Towards the mathematical foundation of the minimum enclosing ball and related problems

arXiv: https://arxiv.org/abs/2402.06629 · HTML: https://mlsanity.com/paper/2402.06629/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 162 references that are in the map.
- First posted on arXiv 9 Jan 2024.

## Builds on (most cited first, 11 of 11)

- [Differentially Private Clustering: Tight Approximation Ratios](https://mlsanity.com/paper/2008.08007/) (2020)
- [Hilbert geometry of the Siegel disk: The Siegel-Klein disk model](https://mlsanity.com/paper/2004.08160/) (2020)
- [Hardness of Approximation of Euclidean k-Median](https://mlsanity.com/paper/2011.04221/) (2020)
- [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)
- [A Differentially Private Linear-Time fPTAS for the Minimum Enclosing Ball Problem](https://mlsanity.com/paper/2206.03319/) (2022)
- [Generalization of the Apollonius theorem for simplices and related problems](https://mlsanity.com/paper/2401.03232/) (2024)
- [Smallest k-Enclosing Rectangle Revisited](https://mlsanity.com/paper/1903.06785/) (2019)
- [Experiments with Unit Disk Cover Algorithms for Covering Massive Pointsets](https://mlsanity.com/paper/2205.01716/) (2022)
- [On the Width of the Regular n-Simplex](https://mlsanity.com/paper/2301.02616/) (2023)

## Built on by (most cited first, 1 of 1)

- [Towards the methodology for solving the minimum enclosing ball and related problems](https://mlsanity.com/paper/2410.11063/) (2024)

## Abstract (arXiv)

Theoretical background is provided towards the mathematical foundation 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. The study of several problems that are similar or related to the minimum enclosing ball problem has received a considerable impetus from the large amount of applications of these problems in various fields of science and technology. The proposed theoretical framework is based on several enclosing (covering) and partitioning (clustering) theorems and provides among others bounds and relations between the circumradius, inradius, diameter and width of a set. These enclosing and partitioning theorems are considered as cornerstones in the field that strongly influencing developments and generalizations to other spaces and non-Euclidean geometries.