{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article10773","name":"Near Isometric Terminal Embeddings for Doubling Metrics","abstract":"Given a metric space (X,d), a set of terminals K subseteq X, and a parameter t >= 1, we consider metric structures (e.g., spanners, distance oracles, embedding into normed spaces) that preserve distances for all pairs in K x X up to a factor of t, and have small size (e.g. number of edges for spanners, dimension for embeddings). While such terminal (aka source-wise) metric structures are known to exist in several settings, no terminal spanner or embedding with distortion close to 1, i.e., t=1+epsilon for some small 0