Euclidean distortion and the sparsest cut

We prove that every n-point metric space of negative type (and, in particular, every npoint subset of L1) embeds into a Euclidean space with distortion O( log n ? log log n), a result which is tight up to the iterated logarithm factor. As a consequence, we obtain the best known polynomial-time approximation algorithm algorithm for the Sparsest Cut problem with general demands. If the demand is supported on a subset of size k, we achieve an approximation ratio of O( log k ? log log k).

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Sanjeev Arora, James R. Lee, Assaf Naor
• Keywords: Algorithms, Iterated Logarithm Factor, N-point Metric Space, Sparsest Cut Problem, STOC 2005