How to get close to the median shape

@article{HarPeled2007HowTG,
  title={How to get close to the median shape},
  author={Sariel Har-Peled},
  journal={Comput. Geom.},
  year={2007},
  volume={36},
  pages={39-51}
}
In this paper, we study the problem of L1-fitting a shape to a set of n points in IR (where d 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 O(n+poly(log n, 1/ε)), where poly(log n, 1/ε) is a polynomial of constant degree of log n and 1/ε (the power of the polynomial is a function of d… CONTINUE READING

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