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arXiv · 2503.20299

Finding Near-Optimal Maximum Set of Disjoint $k$-Cliques in Real-World Social Networks

Wenqing Lin·Xin Chen·Haoxuan Xie·Sibo Wang·Siqiang Luo
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Abstract

A $k$-clique is a dense graph, consisting of $k$ fully-connected nodes, that finds numerous applications, such as community detection and network analysis. In this paper, we study a new problem, that finds a maximum set of disjoint $k$-cliques in a given large real-world graph with a user-defined fixed number $k$, which can contribute to a good performance of teaming collaborative events in online games. However, this problem is NP-hard when $k \geq 3$, making it difficult to solve. To address that, we propose an efficient lightweight method that avoids significant overheads and achieves a $k$-approximation to the optimal, which is equipped with several optimization techniques, including the ordering method, degree estimation in the clique graph, and a lightweight implementation. Besides, to handle dynamic graphs that are widely seen in real-world social networks, we devise an efficient indexing method with careful swapping operations, leading to the efficient maintenance of a near-optimal result with frequent updates in the graph. In various experiments on several large graphs, our proposed approaches significantly outperform the competitors by up to 2 orders of magnitude in running time and 13.3\% in the number of computed disjoint $k$-cliques, which demonstrates the superiority of the proposed approaches in terms of efficiency and effectiveness.

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Wenqing Lin, Xin Chen, Haoxuan Xie, Sibo Wang, Siqiang Luo. 2025-03-26. Finding Near-Optimal Maximum Set of Disjoint $k$-Cliques in Real-World Social Networks. https://arxiv.org/abs/2503.20299

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