Online embedding of metrics

03/28/2023

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by   Ilan Newman, et al.

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We study deterministic online embeddings of metrics spaces into normed spaces and into trees against an adaptive adversary. Main results include a polynomial lower bound on the (multiplicative) distortion of embedding into Euclidean spaces, a tight exponential upper bound on embedding into the line, and a (1+ϵ)-distortion embedding in ℓ_∞ of a suitably high dimension.