Online embedding of metrics

Abstract

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 $(1+\hat{I}\mu )$-distortion embedding in ${\ell }_{\infty }$ of a suitably high dimension.

15 pages, no figures