Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut

Abstract

In this paper, we study the metrics of negative type, which are metrics (V, d) such that √d is an Euclidean metric; these metrics are thus also known as l2-squared metrics.We show how to embed n-point negative-type metrics into Euclidean space l2 with distortion D = O(log3/4n). This embedding result, in turn, implies an O(log3/4k)-approximation algorithm for the Sparsest Cut problem with non-uniform demands. Another corollary we obtain is that n-point subsets of l1 embed into l2 with distortion O(log3/4n).