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Abstract

An algorithm is presented that, given a set of $n$ points in the plane and an integer $k$, $2 \leq k \leq n$, finds $k$ points with a smallest enclosing axes-parallel square. The algorithm has a running time of $O(n \log n + kn \log^{2} k)$ and uses $O(n)$ space. The previously best known algorithm for this problem takes $O(k^{2} n \log n)$ time and uses $O(kn)$ space.