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Abstract: These are notes from talks given at ICMS, Edinburgh, 4-2007 -Geometry andAlgorithms workshop- and at Bernoulli Center, Lausanne 5-2007 -Limits ofgraphs in group theory and computer science-. We survey the following type ofdichotomies exhibited by certain classes X of finite metric spaces: For everyhost space H, either all metrics in X embed almost isometrically in H, or thedistortion of embedding some metrics of X in H is unbounded.

Author: Manor Mendel


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