How to get close to the median shape

  title={How to get close to the median shape},
  author={Sariel Har-Peled},
  booktitle={Symposium on Computational Geometry},
In this paper, we study the problem of <i>L</i><sub>1</sub>-fitting a shape to a set of <i>n</i> points in <i>R<sup>d</sup></i> (where <i>d</i> is a fixed constant), where the target is to minimize the sum of distances of the points to the shape, or alternatively the sum of squared distances. We present a general technique for computing a (1+ε)-approximation for such a problem, with running time <i>O(n</i>+poly(log <i>n</i>, 1/ε)), where poly(log <i>n</i>, 1/ε) is a polynomial of constant… CONTINUE READING