## Computer Science Department

1-2000

Article

#### Abstract or Description

We consider embedding metrics induced by trees into Euclidean spaces with a restricted number of dimensions. We show that any weighted tree T with n vertices and L leaves can be embedded into d -dimensional Euclidean space with Õ (L 1/(d-1) ) distortion. Furthermore, we exhibit an embedding with almost the same distortion which can be computed efficiently. This distortion substantially improves the previous best upper bound of \tilde O (n 2/d ) and almost matches the best known lower bound of Ω(L 1/d ) .

#### DOI

10.1007/s004540010020

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