Abstract

Let P be a set of n points in IRd, and for any integer 0 < = k < = d- 1, let RDk(P) denote the minimum over all k-flats F of maxp2P dist(p, F). We present an algorithm that computes, for any 0 < &quot; < 1, a k-flat that is within a distance of (1 + &quot;)RDk(P) from each point of P. The running time of the algorithm is dnO(k/&quot; 5 log(1/&quot;)). The crucial step in obtaining this algorithm is a structural result that says that there is a near-optimal flat that lies in an affine subspace spanned by a small subset of points in P. The size of this "core-set" depends on k and ε but is independent of the dimension. This

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