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

^*Corresponding author for this work

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

11 Scopus citations

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
Externally published	Yes
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

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10.1145/1109557.1109563

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Local versus Global Properties of Metric Spaces Extended abstract

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