TY - JOUR
T1 - Metric Embeddings - Beyond One-Dimensional Distortion
AU - Krauthgamer, Robert
AU - Linial, Nathan
AU - Magen, Avner
PY - 2004/4
Y1 - 2004/4
N2 - 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 [F] 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.
AB - 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 [F] 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.
UR - http://www.scopus.com/inward/record.url?scp=1842765524&partnerID=8YFLogxK
U2 - 10.1007/s00454-003-2872-2
DO - 10.1007/s00454-003-2872-2
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AN - SCOPUS:1842765524
SN - 0179-5376
VL - 31
SP - 339
EP - 356
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 3
ER -