Local versus Global Properties of Metric Spaces Extended abstract

Sanjeev Arora; László Lovászt; Ilan Newman; Yuval Rabani; Yuri Rabinovich; Santosh Vempala

doi:10.1145/1109557.1109563

Local versus Global Properties of Metric Spaces Extended abstract

Sanjeev Arora
, László Lovászt
, Ilan Newman
, Yuval Rabani
, Yuri Rabinovich
, Santosh Vempala

Department of Computer Science

Research output: Contribution to conference › Paper › peer-review

Abstract

Motivated by applications in combinatorial optimization, we initiate a study of the extent to which the global properties of a metric space (especially, embeddability in ℓ ₁ with low distortion) are determined by the properties of small subspaces. We note connections to similar issues studied already in Ramsey theory, complexity theory (especially PCPs), and property testing. We prove both upper bounds and lower bounds on the distortion of embedding locally constrained metrics into various target spaces.

Original language	English
Pages	41-50
Number of pages	10
DOIs	https://doi.org/10.1145/1109557.1109563
State	Published - 2006
Event	Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms - Miami, FL, United States Duration: 22 Jan 2006 → 24 Jan 2006

Conference

Conference	Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms
Country/Territory	United States
City	Miami, FL
Period	22/01/06 → 24/01/06

ASJC Scopus subject areas

Software
General Mathematics

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10.1145/1109557.1109563

Cite this

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title = "Local versus Global Properties of Metric Spaces Extended abstract",

abstract = "Motivated by applications in combinatorial optimization, we initiate a study of the extent to which the global properties of a metric space (especially, embeddability in ℓ 1 with low distortion) are determined by the properties of small subspaces. We note connections to similar issues studied already in Ramsey theory, complexity theory (especially PCPs), and property testing. We prove both upper bounds and lower bounds on the distortion of embedding locally constrained metrics into various target spaces.",

author = "Sanjeev Arora and L{\'a}szl{\'o} Lov{\'a}szt and Ilan Newman and Yuval Rabani and Yuri Rabinovich and Santosh Vempala",

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AU - Arora, Sanjeev

AU - Lovászt, László

AU - Newman, Ilan

AU - Rabani, Yuval

AU - Rabinovich, Yuri

AU - Vempala, Santosh

PY - 2006

Y1 - 2006

N2 - Motivated by applications in combinatorial optimization, we initiate a study of the extent to which the global properties of a metric space (especially, embeddability in ℓ 1 with low distortion) are determined by the properties of small subspaces. We note connections to similar issues studied already in Ramsey theory, complexity theory (especially PCPs), and property testing. We prove both upper bounds and lower bounds on the distortion of embedding locally constrained metrics into various target spaces.

AB - Motivated by applications in combinatorial optimization, we initiate a study of the extent to which the global properties of a metric space (especially, embeddability in ℓ 1 with low distortion) are determined by the properties of small subspaces. We note connections to similar issues studied already in Ramsey theory, complexity theory (especially PCPs), and property testing. We prove both upper bounds and lower bounds on the distortion of embedding locally constrained metrics into various target spaces.

UR - https://www.scopus.com/pages/publications/33244474846

U2 - 10.1145/1109557.1109563

DO - 10.1145/1109557.1109563

M3 - Paper

AN - SCOPUS:33244474846

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T2 - Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 22 January 2006 through 24 January 2006

ER -

Local versus Global Properties of Metric Spaces Extended abstract

Abstract

Conference

ASJC Scopus subject areas

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