Work

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

Year: 2008

Type: article

Abstract: In this article, we study metrics of negative type , which are metrics ( V , d) such that √d is an Euclidean metric; these metrics are thus also known as ℓ 2 -squared metrics. We show how to embed n -point negative-type metrics into Euclidean space ℓ 2 with distortion D = O (log 3/4 n ). This embedding result, in turn, implies an O (log 3/4 k )-approximation algorithm for the Sparsest Cut problem with nonuniform demands. Another corollary we obtain is that n -point subsets of ℓ 1 embed into ℓ 2 with distortion O (log 3/4 n ).

Source: ACM Transactions on Algorithms

DOI: 10.1145/1361192.1361199

Authors: Shuchi Chawla, Anupam Gupta, Harald Räcke

Institutions: University of Wisconsin–Madison, Carnegie Mellon University, University of Warwick

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Division of Computing and Communication Foundations

Awards: ITR/SY+IM+AP: Center for Applied Algorithms, G7491958520