On Euclidean Embeddings and Bandwidth Minimization

We study Euclidean embeddings of Euclidean metrics and present the following four results: (1) an O(log3 n √ log log n) approximation for minimum bandwidth in conjunction with a semi-definite relaxation, (2) an O(log3 n) approximation in O(nlog n ) time using a new constraint set, (3) a lower bound of Θ( √ log n) on the least possible volume distortion for Euclidean metrics, (4) a new embedding with O( √ log n) distortion of point-to-subset distances.

• Type: Conference
• Year: 2001
• Where: RANDOM
• Authors: John Dunagan, Santosh Vempala
• Keywords: Euclidean Embeddings, Euclidean Metrics, Log N, RANDOM 2001, Theoretical Computer Science