## Abstract

We introduce and study a class l^{dom}_{1} (ρ) of l_{1}-embeddable metrics corresponding to a given metric ρ. This class is defined as the set of all convex combinations of ρ-dominated line metrics. Such metrics were implicitly used before in several constuctions of low-distortion embeddings into l_{p}-spaces, such as Bourgain's embedding of an arbitrary metric ρ on n points with O(log n) distortion. Our main result is that the gap between the distortions of embedding of a finite metric ρ of size n into l_{2} versus into l^{dom}_{1}(ρ) ia at most O(√log n), and that this bound is essentially tight. A significant part of the paper is devoted to proving lower bounds on distortion of such embeddings. We also discuss some general properties and concrete examples.

Original language | English |
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Pages (from-to) | 285-301 |

Number of pages | 17 |

Journal | Israel Journal of Mathematics |

Volume | 123 |

DOIs | |

State | Published - 2001 |

## ASJC Scopus subject areas

- Mathematics (all)

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