Packing Ellipsoids and Chromosomes

Problems of packing shapes with maximal density, possibly into a container of restricted size, are classical in discrete mathematics. We describe here the problem of packing ellipsoids of
given (but varying) dimensions into a finite container, in a way that minimizes the maximum overlap between adjacent ellipsoids. A bilevel optimization algorithm is described for finding local solutions, for both the general case and the easier special case in which the ellipsoids are spheres. Algorithm and analysis tools from semidefinite programming and trust-region methods are key to the approach. We apply the method to the problem of chromosome arrangement in cell nuclei, and compare our results with the experimental observations reported in the biological literature. (Joint work with Caroline Uhler, IST Austria)
September 12 @ 12:30
12:30 pm (1h)

Discovery Building, Orchard View Room

Stephen Wright