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 Abstract: Motivated by applications in combinatorial optimization, we study the extent to which the global properties of a metric space, and especially its embeddability into $\ell_1$ with low distortion, are determined by the properties of its small subspaces. We establish both upper and lower bounds on the distortion of embedding locally constrained metrics into various target spaces. Other aspects of locally constrained metrics are studied as well, in particular, how far are those metrics from general metrics. Publication Date: 2012 Citation: Arora, Sanjeev, László Lovász, Ilan Newman, Yuval Rabani, Yuri Rabinovich, and Santosh Vempala. "Local Versus Global Properties of Metric Spaces." SIAM Journal on Computing 41, no. 1 (2012): pp. 250-271. doi:10.1137/090780304 DOI: 10.1137/090780304 ISSN: 0097-5397 EISSN: 1095-7111 Pages: 250 - 271 Type of Material: Journal Article Journal/Proceeding Title: SIAM Journal on Computing Version: Final published version. Article is made available in OAR by the publisher's permission or policy.