Local versus Global Properties of Metric Spaces Extended 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 `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. ∗Computer Science Department, Princeton University. Supported by David and Lucile Packard Fellowship and NSF grant CCR 0205594. Email: arora@cs.princeton.edu †Microsoft Research and Eötvös Loránd University. Email: lovasz@microsoft.com ‡Computer Science Department, University of Haifa, Haifa 31905, Israel. Email: ilan@cs.haifa.ac.il. §Computer Science Department, Technion, Haifa 32000, Israel. Email: rabani@cs.technion.ac.il. ¶Computer Science Department, University of Haifa, Haifa 31905, Israel. Supported in part by a grant ISF-247-02-10.5. Email: yuri@cs.haifa.ac.il. ‖Mathematics Department, MIT. Supported in part by NSF CCR-0312339 and a Sloan foundation fellowship. Email: vempala@math.mit.edu

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