research-article

Expander flows, geometric embeddings and graph partitioning

Authors:

Umesh VaziraniAuthors Info & Claims

Journal of the ACM (JACM), Volume 56, Issue 2

Article No.: 5, Pages 1 - 37

https://doi.org/10.1145/1502793.1502794

Published: 17 April 2009 Publication History

Abstract

We give a O(√log n)-approximation algorithm for the sparsest cut, edge expansion, balanced separator, and graph conductance problems. This improves the O(log n)-approximation of Leighton and Rao (1988). We use a well-known semidefinite relaxation with triangle inequality constraints. Central to our analysis is a geometric theorem about projections of point sets in R^d, whose proof makes essential use of a phenomenon called measure concentration.

We also describe an interesting and natural “approximate certificate” for a graph's expansion, which involves embedding an n-node expander in it with appropriate dilation and congestion. We call this an expander flow.

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Index Terms

Expander flows, geometric embeddings and graph partitioning
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms

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cover image Journal of the ACM

Journal of the ACM Volume 56, Issue 2

April 2009

190 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/1502793

Issue’s Table of Contents

Copyright © 2009 ACM.

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Publication History

Published: 17 April 2009

Accepted: 01 December 2008

Revised: 01 July 2008

Received: 01 April 2007

Published in JACM Volume 56, Issue 2

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