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Index-based top k α-maximal-clique enumeration over uncertain graphs

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Abstract

Uncertain graphs are widespread in the real world. Enumerating maximal cliques over uncertain graphs is a fundamental problem in many applications. This paper studies the problem of enumerating the top \(k\) maximal cliques with the most number of vertices satisfying that their probabilities \(\ge \alpha\), where each maximal clique is called an \(\alpha\)-maximal-clique. Existing works are inefficient due to suffering from expensive computations on the cliques carrying little information. To address this problem, we propose an index-based top \(k\)  \(\alpha\)-maximal-clique enumeration algorithm which computes \(\alpha\)-maximal-cliques based on an index to improve the efficiency. We propose two efficient indexes, called degree-based index and core-based index, which sort the vertices in descending order according to their degrees or core numbers to help prune unpromising vertices, such that to avoid enumerating redundant \(\alpha\)-maximal-cliques. We propose a support-based pruning strategy to further avoid enumerating the not chosen \(\alpha\)-maximal-cliques to speed up the enumeration. The experimental results on 20 real-world datasets show that our algorithms can return the top \(k\)  \(\alpha\)-maximal-cliques efficiently.

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Acknowledgements

This work was partly supported by grants from the Natural Science Foundation of Shanghai (No. 20ZR1402700) and from the Natural Science Foundation of China (No.: 61472339, 61873337).

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Author notes

  1. Ming Du and Ziyang Chen have equally contributed to this work.

Authors and Affiliations

  1. School of Computer Science and Technology, Donghua University, 2999 Renmin North Road, Songjiang District, Shanghai, 201620, China

    Jing Bai, Junfeng Zhou & Ming Du

  2. College of Information Technology, Shanghai Jian Qiao University, 1111 Hucheng Ring Road, Pudong New Area, Shanghai, 201306, China

    Jing Bai

  3. Shanghai Lixin University of Accounting and Finance, 2800 Wenxiang Road, Songjiang District, Shanghai, 201620, China

    Ziyang Chen

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  1. Jing Bai
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Correspondence to Jing Bai or Junfeng Zhou.

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Bai, J., Zhou, J., Du, M. et al. Index-based top k α-maximal-clique enumeration over uncertain graphs. J Supercomput 78, 19372–19400 (2022). https://doi.org/10.1007/s11227-022-04613-1

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