Article

Euclidean distortion and the sparsest cut

Authors:

Assaf NaorAuthors Info & Claims

STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing

Pages 553 - 562

https://doi.org/10.1145/1060590.1060673

Published: 22 May 2005 Publication History

Abstract

We prove that every n-point metric space of negative type (in particular, every n-point subset of L₁) embeds into a Euclidean space with distortion O(√log n log log n), a result which is tight up to the O(log log n) factor. As a consequence, we obtain the best known polynomial-time approximation 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).

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Cited By

Anand ALee ELi JSaranurak TMohar BShinkar IO'Donnell R(2024)Approximating Small Sparse CutsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649747(319-330)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649747
Chatzikokolakis KCherubin GPalamidessi CTroncoso C(2023)Bayes Security: A Not So Average Metric2023 IEEE 36th Computer Security Foundations Symposium (CSF)10.1109/CSF57540.2023.00011(388-406)Online publication date: Jul-2023
https://doi.org/10.1109/CSF57540.2023.00011
Mu LSugumaran VWang F(2019)A Hybrid Genetic Algorithm for Software Architecture Re-ModularizationInformation Systems Frontiers10.1007/s10796-019-09906-0Online publication date: 17-Apr-2019
https://doi.org/10.1007/s10796-019-09906-0
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Index Terms

Euclidean distortion and the sparsest cut
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing

May 2005

778 pages

ISBN:1581139608

DOI:10.1145/1060590

General Chair:
Hal Gabow
University of Colorado
,
Program Chair:
Ronald Fagin
IBM Almaden Research Center

Copyright © 2005 ACM.

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Published: 22 May 2005

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May 22 - 24, 2005

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Anand ALee ELi JSaranurak TMohar BShinkar IO'Donnell R(2024)Approximating Small Sparse CutsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649747(319-330)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649747
Chatzikokolakis KCherubin GPalamidessi CTroncoso C(2023)Bayes Security: A Not So Average Metric2023 IEEE 36th Computer Security Foundations Symposium (CSF)10.1109/CSF57540.2023.00011(388-406)Online publication date: Jul-2023
https://doi.org/10.1109/CSF57540.2023.00011
Mu LSugumaran VWang F(2019)A Hybrid Genetic Algorithm for Software Architecture Re-ModularizationInformation Systems Frontiers10.1007/s10796-019-09906-0Online publication date: 17-Apr-2019
https://doi.org/10.1007/s10796-019-09906-0
Garber DHazan E(2016)Sublinear time algorithms for approximate semidefinite programmingMathematical Programming: Series A and B10.1007/s10107-015-0932-z158:1-2(329-361)Online publication date: 1-Jul-2016
https://dl.acm.org/doi/10.1007/s10107-015-0932-z
Chawla S(2016)Sparsest CutEncyclopedia of Algorithms10.1007/978-1-4939-2864-4_388(2043-2045)Online publication date: 22-Apr-2016
https://doi.org/10.1007/978-1-4939-2864-4_388
Konjevod G(2016)Separators in GraphsEncyclopedia of Algorithms10.1007/978-1-4939-2864-4_362(1941-1945)Online publication date: 22-Apr-2016
https://doi.org/10.1007/978-1-4939-2864-4_362
Chuzhoy JMakarychev YVijayaraghavan AZhou Y(2015)Approximation Algorithms and Hardness of the k-Route Cut ProblemACM Transactions on Algorithms10.1145/264481412:1(1-40)Online publication date: 31-Dec-2015
https://dl.acm.org/doi/10.1145/2644814
Makarychev KMakarychev YVijayaraghavan AChekuri C(2014)Bilu-linial stable instances of max cut and minimum multiway cutProceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms10.5555/2634074.2634141(890-906)Online publication date: 5-Jan-2014
https://dl.acm.org/doi/10.5555/2634074.2634141
Khandekar RKortsarz GMirrokni V(2014)On the Advantage of Overlapping Clusters for Minimizing ConductanceAlgorithmica10.1007/s00453-013-9761-869:4(844-863)Online publication date: 1-Aug-2014
https://dl.acm.org/doi/10.1007/s00453-013-9761-8
Kane DMeka RBoneh DRoughgarden TFeigenbaum J(2013)A PRG for lipschitz functions of polynomials with applications to sparsest cutProceedings of the forty-fifth annual ACM symposium on Theory of Computing10.1145/2488608.2488610(1-10)Online publication date: 1-Jun-2013
https://dl.acm.org/doi/10.1145/2488608.2488610
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