Efficient simple (1+ε)-approximation of the minimum-volume bounding ellipsoid in 3D

Design an efficient and simple algorithm that computes a (1+ε)-approximation of the minimum-volume bounding ellipsoid of a finite set of points in three-dimensional Euclidean space.

Background

While the paper focuses on approximating the minimum-volume bounding box in R3, many applications may benefit from ellipsoidal bounds, which can better fit certain point distributions.

The authors highlight the need for an efficient and simple (1+ε)-approximation algorithm for the minimum-volume bounding ellipsoid in R3, indicating that such a practical method is not currently established within the scope of their work.

References

We conclude by mentioning two open problems:

  • Can one compute efficiently and by a simple algorithm a $(1 + )$-approximation of the minimum-volume bounding ellipsoid of a point set in $R3$?
— Efficiently Approximating the Minimum-Volume Bounding Box of a Point Set in Three Dimensions  (2512.12391 - Barequet et al., 13 Dec 2025) in Conclusion (Section: Conclusion)