Terminal Embeddings in Sublinear Time

arXiv:2110.08691v3 Announce Type: replace-cross
Abstract: Recently (Elkin, Filtser, Neiman 2017) introduced the concept of a {\it terminal embedding} from one metric space $(X,d_X)$ to another $(Y,d_Y)$ with a set of designated terminals $T\subset X$. Such an embedding $f$ is said to have distortion $\rho\ge 1$ if $\rho$ is the smallest value such that there exists a constant $C>0$ satisfying
\begin{equation*}
\forall x\in T\ \forall q\in X,\ C d_X(x, q) \le d_Y(f(x), f(q)) \le C \rho d_X(x, q) .
\end{equation*}
When …

abstract arxiv concept cs.cg cs.ds cs.lg embedding embeddings set space stat.ml terminal type value