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

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 " 2-squared" metrics. We show how to embed n-point negative-type metrics into Euclidean space 2 with distortion D = O(log3/4 n). This embedding result, in turn, implies an O(log3/4 k)-approximation algorithm for the Sparsest Cut problem with non-uniform demands. Another corollary we obtain is that n-point subsets of 1 embed into 2 with distortion O(log3/4 n).

• Type: Journal
• Year: 2008
• Where: TALG
• Authors: Shuchi Chawla, Anupam Gupta, Harald Räcke
• Keywords: Euclidean Metric, N-point Negative-type Metrics, Negative Type, TALG 2008