Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut

@article{Chawla2005EmbeddingsON,
  title={Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut},
  author={Shuchi Chawla and Anupam Gupta and Harald R{\"a}cke},
  journal={ACM Trans. Algorithms},
  year={2005},
  volume={4},
  pages={22:1-22:18}
}
In this article, we study metrics of <i>negative type</i>, which are metrics (<i>V</i>, d) such that &sqrt;d is an Euclidean metric; these metrics are thus also known as ℓ<sub>2</sub>-squared metrics. We show how to embed <i>n</i>-point negative-type metrics into Euclidean space ℓ<sub>2</sub> with distortion <i>D</i> = <i>O</i>(log<sup>3/4</sup><i>n</i>). This embedding result, in turn, implies an <i>O</i>(log<sup>3/4</sup><i>k</i>)-approximation algorithm for the Sparsest Cut problem with… CONTINUE READING

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