research-article

On partitioning graphs via single commodity flows

Authors:

Lorenzo Orecchia,

Leonard J. Schulman,

Umesh V. Vazirani,

Nisheeth K. VishnoiAuthors Info & Claims

STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing

Pages 461 - 470

https://doi.org/10.1145/1374376.1374442

Published: 17 May 2008 Publication History

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Abstract

In this paper we obtain improved upper and lower bounds for the best approximation factor for Sparsest Cut achievable in the cut-matching game framework proposed in Khandekar et al. [9]. We show that this simple framework can be used to design combinatorial algorithms that achieve O(log n) approximation factor and whose running time is dominated by a poly-logarithmic number of single-commodity max-flow computations. This matches the performance of the algorithm of Arora and Kale [2]. Moreover, we also show that it is impossible to get an approximation factor of better than Ω(√log n) in the cut-matching game framework. These results suggest that the simple and concrete abstraction of the cut-matching game may be powerful enough to capture the essential features of the complexity of Sparsest Cut.

References

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Cited By

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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
Veldt N(2023)Cut-matching Games for Generalized Hypergraph Ratio CutsProceedings of the ACM Web Conference 202310.1145/3543507.3583539(694-704)Online publication date: 30-Apr-2023
https://dl.acm.org/doi/10.1145/3543507.3583539
Brand JChen LKyng RLiu YPeng RGutenberg MSachdeva SSidford A(2023)A Deterministic Almost-Linear Time Algorithm for Minimum-Cost Flow2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00037(503-514)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00037
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Index Terms

On partitioning graphs via single commodity flows
1. Theory of computation
  1. Design and analysis of algorithms

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Graph partitioning using single commodity flows

We show that the sparsest cut in graphs with n vertices and m edges can be approximated within O(log² n) factor in Õ(m + n^3/2) time using polylogarithmic single commodity max-flow computations. Previous algorithms are based on multicommodity flows that ...
Expander flows, geometric embeddings and graph partitioning

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 ...
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We show that the sparsest cut in graphs can be approximated within O(log² n) factor in Õ(n^3/2) time using polylogarithmic single commodity max-flow computations. Previous algorithms are based on multicommodity flows which take time Õ(n²). Our algorithm ...

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Published In

STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing

May 2008

712 pages

ISBN:9781605580470

DOI:10.1145/1374376

General Chair:
Richard Ladner
University of Washington
,
Program Chair:
Cynthia Dwork
Microsoft Research, Silicon Valley

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 May 2008

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STOC '08: Symposium on Theory of Computing

May 17 - 20, 2008

British Columbia, Victoria, Canada

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STOC '08 Paper Acceptance Rate 80 of 325 submissions, 25%;

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

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Cited By

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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
Veldt N(2023)Cut-matching Games for Generalized Hypergraph Ratio CutsProceedings of the ACM Web Conference 202310.1145/3543507.3583539(694-704)Online publication date: 30-Apr-2023
https://dl.acm.org/doi/10.1145/3543507.3583539
Brand JChen LKyng RLiu YPeng RGutenberg MSachdeva SSidford A(2023)A Deterministic Almost-Linear Time Algorithm for Minimum-Cost Flow2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00037(503-514)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00037
Chen LPeng RWang D(2022)2-norm Flow Diffusion in Near-Linear Time2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00060(540-549)Online publication date: Mar-2022
https://doi.org/10.1109/FOCS52979.2021.00060
Vishnoi N(2021)Algorithms for Convex Optimization10.1017/9781108699211Online publication date: 24-Sep-2021
https://doi.org/10.1017/9781108699211
Saranurak TWang DChan T(2019)Expander decomposition and pruningProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310597(2616-2635)Online publication date: 6-Jan-2019
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Priyadarshini SRodda S(2019)Geometric Multi-Way Frequent Subgraph Mining Approach to a Single Large DatabaseSmart Intelligent Computing and Applications10.1007/978-981-32-9690-9_23(233-244)Online publication date: 4-Oct-2019
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Chattopadhyay ALangberg MLi SRudra AKlein P(2017)Tight network topology dependent bounds on rounds of communicationProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039853(2524-2539)Online publication date: 16-Jan-2017
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Henzinger MRao SWang DKlein P(2017)Local flow partitioning for faster edge connectivityProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039811(1919-1938)Online publication date: 16-Jan-2017
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Fountoulakis KGleich DMahoney M(2017)An Optimization Approach to Locally-Biased Graph AlgorithmsProceedings of the IEEE10.1109/JPROC.2016.2637349105:2(256-272)Online publication date: Mar-2017
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