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A New Dynamic Algorithm for Densest Subhypergraphs

Authors:

Sayan Bhattacharya,

Jayesh Choudhari,

Prantar GhoshAuthors Info & Claims

WWW '22: Proceedings of the ACM Web Conference 2022

Pages 1093 - 1103

https://doi.org/10.1145/3485447.3512158

Published: 25 April 2022 Publication History

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Abstract

Computing a dense subgraph is a fundamental problem in graph mining, with a diverse set of applications ranging from electronic commerce to community detection in social networks. In many of these applications, the underlying context is better modelled as a weighted hypergraph that keeps evolving with time.

This motivates the problem of maintaining the densest subhypergraph of a weighted hypergraph in a dynamic setting, where the input keeps changing via a sequence of updates (hyperedge insertions/deletions). Previously, the only known algorithm for this problem was due to Hu et al. [19]. This algorithm worked only on unweighted hypergraphs, and had an approximation ratio of (1 +ϵ)r2 and an update time of O(poly(r, log n)), where r denotes the maximum rank of the input across all the updates.

We obtain a new algorithm for this problem, which works even when the input hypergraph is weighted. Our algorithm has a significantly improved (near-optimal) approximation ratio of (1 +ϵ) that is independent of r, and a similar update time of O(poly(r, log n)). It is the first (1 +ϵ)-approximation algorithm even for the special case of weighted simple graphs.

To complement our theoretical analysis, we perform experiments with our dynamic algorithm on large-scale, real-world data-sets. Our algorithm significantly outperforms the state of the art [19] both in terms of accuracy and efficiency.

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Cited By

Lanciano TMiyauchi AFazzone ABonchi F(2024)A Survey on the Densest Subgraph Problem and its VariantsACM Computing Surveys10.1145/365329856:8(1-40)Online publication date: 30-Apr-2024
https://dl.acm.org/doi/10.1145/3653298
Balalau OBonchi FChan TGullo FSozio MXie H(2024)Finding Subgraphs with Maximum Total Density and Limited Overlap in Weighted HypergraphsACM Transactions on Knowledge Discovery from Data10.1145/363941018:4(1-21)Online publication date: 12-Feb-2024
https://dl.acm.org/doi/10.1145/3639410
Xu YMa CFang YBao Z(2024)Efficient and effective algorithms for densest subgraph discovery and maintenanceThe VLDB Journal10.1007/s00778-024-00855-y33:5(1427-1452)Online publication date: 8-May-2024
https://doi.org/10.1007/s00778-024-00855-y
Show More Cited By

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cover image ACM Conferences

WWW '22: Proceedings of the ACM Web Conference 2022

April 2022

3764 pages

ISBN:9781450390965

DOI:10.1145/3485447

Editors:
Frédérique Laforest
INSA Lyon, France
,
Raphaël Troncy
EURECOM, France
,
Elena Simperl
King’s College London, UK
,
Deepak Agarwal
Pinterest, USA
,
Aristides Gionis
KTH Royal Institute of Technology, Sweden
,
Ivan Herman
W3C / retired
,
Lionel Médini
Université Lyon 1, France

Copyright © 2022 ACM.

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Published: 25 April 2022

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WWW '22: The ACM Web Conference 2022

April 25 - 29, 2022

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Overall Acceptance Rate 1,899 of 8,196 submissions, 23%

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Cited By

Lanciano TMiyauchi AFazzone ABonchi F(2024)A Survey on the Densest Subgraph Problem and its VariantsACM Computing Surveys10.1145/365329856:8(1-40)Online publication date: 30-Apr-2024
https://dl.acm.org/doi/10.1145/3653298
Balalau OBonchi FChan TGullo FSozio MXie H(2024)Finding Subgraphs with Maximum Total Density and Limited Overlap in Weighted HypergraphsACM Transactions on Knowledge Discovery from Data10.1145/363941018:4(1-21)Online publication date: 12-Feb-2024
https://dl.acm.org/doi/10.1145/3639410
Xu YMa CFang YBao Z(2024)Efficient and effective algorithms for densest subgraph discovery and maintenanceThe VLDB Journal10.1007/s00778-024-00855-y33:5(1427-1452)Online publication date: 8-May-2024
https://doi.org/10.1007/s00778-024-00855-y
Xu YMa CFang YBao Z(2023)Efficient and Effective Algorithms for Generalized Densest Subgraph DiscoveryProceedings of the ACM on Management of Data10.1145/35893141:2(1-27)Online publication date: 20-Jun-2023
https://doi.org/10.1145/3589314
Bhattacharya SBuchbinder NLevin RSaranurak T(2023)Chasing Positive Bodies2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00103(1694-1714)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00103

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