mlsanityData to 14 Oct 2026

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

arXiv 2402.06629 ↗First posted 9 Jan 2024cs.CG cs.AI math.GTcited by 1

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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.

Key facts. Cited by 1 paper 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

11 of 162 references.

References · 11

  1. 2020Differentially Private Clustering: Tight Approximation Ratioscited by 34
  2. 2020Hilbert geometry of the Siegel disk: The Siegel-Klein disk modelcited by 7
  3. 2020Hardness of Approximation of Euclidean k-Mediancited by 5
  4. 2018Theorems of Carath'eodory, Helly, and Tverberg without dimensioncited by 4
  5. 2013Helly-Type Theorems in Property Testingcited by 2
  6. 2017The discrete yet ubiquitous theorems of Carath'eodory, Helly, Sperner, Tucker, and Tverbergcited by 2
  7. 2022A Differentially Private Linear-Time fPTAS for the Minimum Enclosing Ball Problemcited by 2
  8. 2024Generalization of the Apollonius theorem for simplices and related problemscited by 2
  9. 2019Smallest k-Enclosing Rectangle Revisitedcited by 1
  10. 2022Experiments with Unit Disk Cover Algorithms for Covering Massive Pointsetscited by 1
  11. 2023On the Width of the Regular n-Simplexcited by 1

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Citing papers per year: 2024: 1.

1 paper.

  1. 2024Towards the methodology for solving the minimum enclosing ball and related problemscited by 0