Metric Embeddings - Beyond One-Dimensional Distortion.

摘要

Metric spaces and their embeddings have recently played a prominent role in the development of new algorithms. So far, most of the emphasis was on embeddings that preserve pairwise distances. A very intriguing concept introduced by Feige [Fei00], allows us to quantify the extent to which higher-dimensional structures are preserved by a given embedding. We investigate this concept for several basic graph families such as paths, trees, cubes and expanders.