Showing papers by "Yuri Rabinovich published in 2023"
28 Mar 2023
TL;DR: Deterministic online embeddings of metric spaces into normed spaces of various dimensions and into trees are studied to establish some upper and lower bounds on the distortion of such embedding.
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 $(1+\epsilon)$-distortion embedding in $\ell_\infty$ of a suitably high dimension.