Low distortion maps between point sets

@inproceedings{Mathieu2004LowDM,
  title={Low distortion maps between point sets},
  author={Claire Mathieu and Yuval Rabani and Alistair Sinclair},
  booktitle={STOC},
  year={2004}
}
We initiate the study of the minimum distortion problem: given as input two n-point metric spaces, find a bijection between them with minimum distortion. This is an abstraction of certain geometric problems in shape and image matching, and is also a natural variation and extension of the fundamental problems of graph isomorphism and bandwidth. Our focus is on algorithms that find an optimal (or near-optimal) bijection when the distortion is fairly small. We present a polynomial time algorithm… CONTINUE READING

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