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Provably and Efficiently Approximating Near-cliques using the Turán Shadow: PEANUTS

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C. SeshadhriAuthors Info & Claims

WWW '20: Proceedings of The Web Conference 2020

Pages 1966 - 1976

https://doi.org/10.1145/3366423.3380264

Published: 20 April 2020 Publication History

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Abstract

Clique and near-clique counts are important graph properties with applications in graph generation, graph modeling, graph analytics, community detection among others. They are the archetypal examples of dense subgraphs. While there are several different definitions of near-cliques, most of them share the attribute that they are cliques that are missing a small number of edges. Clique counting is itself considered a challenging problem. Counting near-cliques is significantly harder more so since the search space for near-cliques is orders of magnitude larger than that of cliques.

We give a formulation of a near-clique as a clique that is missing a constant number of edges. We exploit the fact that a near-clique contains a smaller clique, and use techniques for clique sampling to count near-cliques. This method allows us to count near-cliques with 1 or 2 missing edges, in graphs with tens of millions of edges. To the best of our knowledge, there was no known efficient method for this problem, and we obtain a 10x − 100x speedup over existing algorithms for counting near-cliques.

Our main technique is a space efficient adaptation of the Turán Shadow sampling approach, recently introduced by Jain and Seshadhri (WWW 2017). This approach constructs a large recursion tree (called the Turán Shadow) that represents cliques in a graph. We design a novel algorithm that builds an estimator for near-cliques, using a online, compact construction of the Turán Shadow.

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Cited By

Zhou YGuo QFang YMa C(2024)A Counting-based Approach for Efficient k-Clique Densest Subgraph DiscoveryProceedings of the ACM on Management of Data10.1145/36549222:3(1-27)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3654922
Ye XLi RDai QChen HWang G(2024)Efficient -Clique Counting on Large Graphs: The Power of Color-Based Sampling ApproachesIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2023.331464336:4(1518-1536)Online publication date: Apr-2024
https://doi.org/10.1109/TKDE.2023.3314643
Megherbi WHaddad MSeba H(2024)DeepDenseExpert Systems with Applications: An International Journal10.1016/j.eswa.2023.121816238:PBOnline publication date: 27-Feb-2024
https://dl.acm.org/doi/10.1016/j.eswa.2023.121816
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Index Terms

Provably and Efficiently Approximating Near-cliques using the Turán Shadow: PEANUTS
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms

Index terms have been assigned to the content through auto-classification.

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cover image ACM Conferences

WWW '20: Proceedings of The Web Conference 2020

April 2020

3143 pages

ISBN:9781450370233

DOI:10.1145/3366423

Editors:
Yennun Huang
Acadmica sinica, Taiwan
,
Irwin King
The Chinese University of Hong Kong, Hong Kong
,
Tie-Yan Liu
Microsoft Research Asia, China
,
Maarten van Steen
University of Twente, Netherlands

Copyright © 2020 ACM.

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Published: 20 April 2020

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WWW '20: The Web Conference 2020

April 20 - 24, 2020

Taipei, Taiwan

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Cited By

Zhou YGuo QFang YMa C(2024)A Counting-based Approach for Efficient k-Clique Densest Subgraph DiscoveryProceedings of the ACM on Management of Data10.1145/36549222:3(1-27)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3654922
Ye XLi RDai QChen HWang G(2024)Efficient -Clique Counting on Large Graphs: The Power of Color-Based Sampling ApproachesIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2023.331464336:4(1518-1536)Online publication date: Apr-2024
https://doi.org/10.1109/TKDE.2023.3314643
Megherbi WHaddad MSeba H(2024)DeepDenseExpert Systems with Applications: An International Journal10.1016/j.eswa.2023.121816238:PBOnline publication date: 27-Feb-2024
https://dl.acm.org/doi/10.1016/j.eswa.2023.121816
He YWang KZhang WLin XZhang Y(2023)Scaling Up k-Clique Densest Subgraph DetectionProceedings of the ACM on Management of Data10.1145/35889231:1(1-26)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.1145/3588923
Ye XLi RDai QChen HWang G(2022)Lightning Fast and Space Efficient k-clique CountingProceedings of the ACM Web Conference 202210.1145/3485447.3512167(1191-1202)Online publication date: 25-Apr-2022
https://dl.acm.org/doi/10.1145/3485447.3512167
Teixeira CKakodkar MDias VMeira WRibeiro B(2022)Sequential stratified regeneration: MCMC for large state spaces with an application to subgraph count estimationData Mining and Knowledge Discovery10.1007/s10618-021-00802-336:1(414-447)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1007/s10618-021-00802-3
Belov DWollack J(2021)Graph Theory Approach to Detect Examinees Involved in Test CollusionApplied Psychological Measurement10.1177/0146621621101390245:4(253-267)Online publication date: 12-May-2021
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