Abstract
We show that every n-point metric of negative type (in particular, every n-point subset of L 1) admits a Fréchet embedding into Euclidean space with distortion \(O(\sqrt{\log n}\cdot \log \log n)\) , a result which is tight up to the O(log log n) factor, even for Euclidean metrics. This strengthens our recent work on the Euclidean distortion of metrics of negative into Euclidean space.
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S. Arora supported by David and Lucile Packard Fellowship and NSF grant CCR-0205594. J.R. Lee supported by NSF grant CCR-0121555, NSF 0514993, NSF 0528414 and an NSF Graduate Research Fellowship.
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Arora, S., Lee, J.R. & Naor, A. Fréchet Embeddings of Negative Type Metrics. Discrete Comput Geom 38, 726–739 (2007). https://doi.org/10.1007/s00454-007-9007-0
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DOI: https://doi.org/10.1007/s00454-007-9007-0