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Fast Maximal Quasi-clique Enumeration: A Pruning and Branching Co-Design Approach

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Cheng LongAuthors Info & Claims

Proceedings of the ACM on Management of Data, Volume 1, Issue 3

Article No.: 211, Pages 1 - 26

https://doi.org/10.1145/3617331

Published: 13 November 2023 Publication History

Abstract

Mining cohesive subgraphs from a graph is a fundamental problem in graph data analysis. One notable cohesive structure is γ-quasi-clique (QC), where each vertex connects at least a fraction γ of the other vertices inside. Enumerating maximal γ-quasi-cliques (MQCs) of a graph has been widely studied and used for many applications such as community detection and significant biomolecule structure discovery. One common practice of finding all MQCs is to (1) find a set of QCs containing all MQCs and then (2) filter out non-maximal QCs. While quite a few algorithms have been developed (which are branch-and-bound algorithms) for finding a set of QCs that contains all MQCs, all focus on sharpening the pruning techniques and devote little effort to improving the branching part. As a result, they provide no guarantee on pruning branches and all have the worst-case time complexity of O*(2n), where O* suppresses the polynomials and n is the number of vertices in the graph. In this paper, we focus on the problem of finding a set of QCs containing all MQCs but deviate from further sharpening the pruning techniques as existing methods do. We pay attention to both the pruning and branching parts and develop new pruning techniques and branching methods that would suit each other better towards pruning more branches both theoretically and practically. Specifically, we develop a new branch-and-bound algorithm called FastQC based on newly developed pruning techniques and branching methods, which improves the worst-case time complexity to O*(αkn), where αk is a positive real number strictly smaller than 2. Furthermore, we develop a divide-and-conquer strategy for boosting the performance of FastQC. Finally, we conduct extensive experiments on both real and synthetic datasets, and the results show that our algorithms are up to two orders of magnitude faster than the state-of-the-art on real datasets.

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Cited By

Liu SZhou JWang DZhang ZLei M(2024)An optimization algorithm for maximum quasi-clique problem based on information feedback modelPeerJ Computer Science10.7717/peerj-cs.217310(e2173)Online publication date: 12-Jul-2024
https://doi.org/10.7717/peerj-cs.2173
Rahman ARoy KMaliha RChowdhury TBaeza-Yates RBonchi F(2024)A Fast Exact Algorithm to Enumerate Maximal Pseudo-cliques in Large Sparse GraphsProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3672066(2479-2490)Online publication date: 25-Aug-2024
https://dl.acm.org/doi/10.1145/3637528.3672066
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
Show More Cited By

Index Terms

Fast Maximal Quasi-clique Enumeration: A Pruning and Branching Co-Design Approach
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms

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Published In

cover image Proceedings of the ACM on Management of Data

Proceedings of the ACM on Management of Data Volume 1, Issue 3

PACMMOD

September 2023

472 pages

EISSN:2836-6573

DOI:10.1145/3632968

Editor:
Divyakant Agrawal
UC Santa Barbara, United States

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Copyright © 2023 ACM.

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Publication History

Published: 13 November 2023

Published in PACMMOD Volume 1, Issue 3

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Cited By

Liu SZhou JWang DZhang ZLei M(2024)An optimization algorithm for maximum quasi-clique problem based on information feedback modelPeerJ Computer Science10.7717/peerj-cs.217310(e2173)Online publication date: 12-Jul-2024
https://doi.org/10.7717/peerj-cs.2173
Rahman ARoy KMaliha RChowdhury TBaeza-Yates RBonchi F(2024)A Fast Exact Algorithm to Enumerate Maximal Pseudo-cliques in Large Sparse GraphsProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3672066(2479-2490)Online publication date: 25-Aug-2024
https://dl.acm.org/doi/10.1145/3637528.3672066
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
Yu KLong C(2023)Fast Maximal Quasi-clique Enumeration: A Pruning and Branching Co-Design ApproachProceedings of the ACM on Management of Data10.1145/36173311:3(1-26)Online publication date: 13-Nov-2023
https://dl.acm.org/doi/10.1145/3617331

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