Packing Ellipsoids with Overlap ∗ Caroline Uhler

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.