Metric Embeddings—Beyond One-Dimensional Distortion

Authors:
Robert Krauthgamer;Nathan Linial;Avner Magen
Affiliations:
International Computer Science Institute and Computer Science Division, University of California, Berkeley, CA 94720, USA;School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel;Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4
Venue:
Discrete & Computational Geometry
Year:
2004

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Abstract

The extensive study of metric spaces and their embeddings has so far focused on embeddings that preserve pairwise distances. A very intriguing concept introduced by Feige allows us to quantify the extent to which larger structures are preserved by a given embedding. We investigate this concept, focusing on several major graph families such as paths, trees, cubes, and expanders. We find some similarities to the regular (pairwise) distortion, as well as some striking differences.