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We present an algorithm that gives a constant factor approximation for the following problem. Given a set of n points in the plane with a Euclidean distance metric and an integer k < n, find the tree of least weight that spans k points. If desired, one may also specify in the problem a "root vertex" that must be in the tree. Our result improves on the previous best bound of O(log k) of Garg and Hochbaum 5, which in turn improved a previous 0(kl/4) bound of Ravi et al 9.
Blum et al. (Sun,) studied this question.