Heuristic approaches to constructing a minimum volume ellipsoid around a subset of points

The paper deals with the following essentially combinatorial problem: Given $N$ points in $\mathbb{R}^n$, compose the ellipsoid of minimum volume containing exactly $N$ – $k$ points where $k$ is much less than $N$. Six algorithms for an approximate solution of this problem are proposed; they are based on certain heuristic considerations. Under various assumptions on the mechanism of generating the points and their amount, the comparative efficiency of the algorithms was conducted and the results of numerical experiments were presented.