Packing ellipsoids with overlap

TL;DR

This paper addresses the challenge of optimally packing ellipsoids within a container to minimize overlaps, presenting algorithms, convergence proofs, and applications to chromosome organization.

Contribution

It introduces a bilevel optimization framework and algorithms for packing ellipsoids, including a simplified method for spherical cases, with theoretical and computational validation.

Findings

Algorithms effectively minimize overlaps in ellipsoid packing

Convergence of the proposed methods is established

Application to chromosome organization demonstrates practical relevance

Abstract

The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact spheres. Convergence results are proved and computational experience is described and illustrated. The motivating application - chromosome organization in the human cell nucleus - is discussed briefly, and some illustrative results are presented.