Euclidean quotients of finite metric spaces

Manor Mendel; Assaf Naor

doi:10.1016/j.aim.2003.12.001

Euclidean quotients of finite metric spaces

Manor Mendel, Assaf Naor

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M and α≥1, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study the analogous problem for embeddings into ℓ_p, and the particular case of the hypercube.

Original language	English (US)
Pages (from-to)	451-494
Number of pages	44
Journal	Advances in Mathematics
Volume	189
Issue number	2
DOIs	https://doi.org/10.1016/j.aim.2003.12.001
State	Published - Dec 20 2004
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1016/j.aim.2003.12.001

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author = "Manor Mendel and Assaf Naor",

note = "Funding Information: ·Corresponding author. Fax: +1-425-936-7329. E-mail addresses: mendelma@cs.huji.ac.il (M. Mendel), anaor@microsoft.com (A. Naor). 1Supported in part by a grant from the Israeli Science Foundation (195/02), and by the Landau Center.",

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N2 - This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M and α≥1, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study the analogous problem for embeddings into ℓp, and the particular case of the hypercube.

AB - This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M and α≥1, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study the analogous problem for embeddings into ℓp, and the particular case of the hypercube.

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Euclidean quotients of finite metric spaces

Abstract

All Science Journal Classification (ASJC) codes

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