research-article

On Directed Densest Subgraph Discovery

Authors:

Laks V. S. Lakshmanan,

Xuemin LinAuthors Info & Claims

ACM Transactions on Database Systems (TODS), Volume 46, Issue 4

Article No.: 13, Pages 1 - 45

https://doi.org/10.1145/3483940

Published: 15 November 2021 Publication History

Abstract

Given a directed graph G, the directed densest subgraph (DDS) problem refers to the finding of a subgraph from G, whose density is the highest among all the subgraphs of G. The DDS problem is fundamental to a wide range of applications, such as fraud detection, community mining, and graph compression. However, existing DDS solutions suffer from efficiency and scalability problems: on a 3,000-edge graph, it takes three days for one of the best exact algorithms to complete. In this article, we develop an efficient and scalable DDS solution. We introduce the notion of [x, y]-core, which is a dense subgraph for G, and show that the densest subgraph can be accurately located through the [x, y]-core with theoretical guarantees. Based on the [x, y]-core, we develop exact and approximation algorithms. We further study the problems of maintaining the DDS over dynamic directed graphs and finding the weighted DDS on weighted directed graphs, and we develop efficient non-trivial algorithms to solve these two problems by extending our DDS algorithms. We have performed an extensive evaluation of our approaches on 15 real large datasets. The results show that our proposed solutions are up to six orders of magnitude faster than the state-of-the-art.

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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
Gao SYu KLiu SLong CQiu Z(2024)On Searching Maximum Directed $(k, \ell)$-Plex2024 IEEE 40th International Conference on Data Engineering (ICDE)10.1109/ICDE60146.2024.00202(2570-2583)Online publication date: 13-May-2024
https://doi.org/10.1109/ICDE60146.2024.00202
Xu YMa CFang YBao Z(2024)Efficient and effective algorithms for densest subgraph discovery and maintenanceThe VLDB Journal10.1007/s00778-024-00855-yOnline publication date: 8-May-2024
https://doi.org/10.1007/s00778-024-00855-y
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Index Terms

On Directed Densest Subgraph Discovery
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Network flows
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis

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cover image ACM Transactions on Database Systems

ACM Transactions on Database Systems Volume 46, Issue 4

December 2021

169 pages

ISSN:0362-5915

EISSN:1557-4644

DOI:10.1145/3492445

Editor:
Christopher Jermaine
Rice University, USA

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Publication History

Published: 15 November 2021

Accepted: 01 August 2021

Revised: 01 July 2021

Received: 01 August 2020

Published in TODS Volume 46, Issue 4

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Research Grants Council of Hong Kong
University of Hong Kong
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HKU-TCL Joint Research Center for Artificial Intelligence
NSFC
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Natural Sciences and Engineering Research Council of Canada (NSERC)
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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
Gao SYu KLiu SLong CQiu Z(2024)On Searching Maximum Directed $(k, \ell)$-Plex2024 IEEE 40th International Conference on Data Engineering (ICDE)10.1109/ICDE60146.2024.00202(2570-2583)Online publication date: 13-May-2024
https://doi.org/10.1109/ICDE60146.2024.00202
Xu YMa CFang YBao Z(2024)Efficient and effective algorithms for densest subgraph discovery and maintenanceThe VLDB Journal10.1007/s00778-024-00855-yOnline publication date: 8-May-2024
https://doi.org/10.1007/s00778-024-00855-y
Luo WYang QFang YZhou X(2023)Efficient Core Maintenance in Large Bipartite GraphsProceedings of the ACM on Management of Data10.1145/36173291:3(1-26)Online publication date: 13-Nov-2023
https://dl.acm.org/doi/10.1145/3617329
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://dl.acm.org/doi/10.1145/3589314
Luo WTang ZFang YMa CZhou X(2023)Scalable Algorithms for Densest Subgraph Discovery2023 IEEE 39th International Conference on Data Engineering (ICDE)10.1109/ICDE55515.2023.00029(287-300)Online publication date: May-2023
https://doi.org/10.1109/ICDE55515.2023.00029
Han T(2023)Efficient Densest Subgraphs Discovery in Large Dynamic Graphs by Greedy ApproximationIEEE Access10.1109/ACCESS.2023.327719711(49367-49377)Online publication date: 2023
https://doi.org/10.1109/ACCESS.2023.3277197
Ma CFang YCheng RLakshmanan LHan XLi X(2023)Accelerating directed densest subgraph queries with software and hardware approachesThe VLDB Journal — The International Journal on Very Large Data Bases10.1007/s00778-023-00805-033:1(207-230)Online publication date: 31-Jul-2023
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Fang YLuo WMa C(2022)Densest subgraph discovery on large graphsProceedings of the VLDB Endowment10.14778/3554821.355489515:12(3766-3769)Online publication date: 1-Aug-2022
https://dl.acm.org/doi/10.14778/3554821.3554895
Ma CCheng RLakshmanan LHan X(2022)Finding locally densest subgraphsProceedings of the VLDB Endowment10.14778/3551793.355182615:11(2719-2732)Online publication date: 1-Jul-2022
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