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Approximate minimum spanning ellipse in the streaming model

In [11] Zarrabi-Zadeh and Chan proposed an algorithm to compute an approximate minimum spanning ball in the streaming model of computation and showed by an elegant analysis that the radius of the approximate ball is to within 3/2 of the exact one. Inspired by this result, in this paper we consider the extension of this result to computing approximate minimum spanning ellipses. The ball algorithm is simple to the point of being trivial, but the extension of the algorithm to ellipses is non-trivial. Surprisingly, the approximation ratio of the areas is not bounded and we provide an elegant proof of this.