Work

Euclidean distortion and the Sparsest Cut

Year: 2005

Type: preprint

Abstract: We prove that every $n$-point metric space of negative type (and, in particular, every $n$-point subset of $L_1$) embeds into a Euclidean space with distortion $O(\sqrt{\log n} \cdot\log \log n)$, a result which is tight up to the iterated logarithm factor. As a consequence, we obtain the best known polynomial-time approximation algorithm for the Sparsest Cut problem with general demands. Namely, if the demand is supported on a subset of size $k$, we achieve an approximation ratio of $O(\sqrt{\log k}\cdot \log \log k)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.math/0508154

Authors: Arora, Sanjeev, Lee, James R., Naor, Assaf

Institutions: Princeton University, University of Washington, Courant Institute of Mathematical Sciences, New York University

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2952787131

Cites: 22

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Related to: 10