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As a fundamental task in graph data management, maximal clique enumeration(MCE) has attracted extensive attention from both academic and industrialcommunities due to its wide range of applications. However, MCE is verychallenging as the number of maximal cliques may grow exponentially with thenumber of vertices. The state-of-the-art methods adopt a recursive paradigm toenumerate maximal cliques exhaustively, suffering from a large amount ofredundant computation. In this paper, we propose a novel reduction-basedframework for MCE, namely RMCE, that aims to reduce the search space andminimize unnecessary computations. The proposed framework RMCE incorporatesthree kinds of powerful reduction techniques including global reduction,dynamic reduction, and maximality check reduction. Global and dynamic reductiontechniques effectively reduce the size of the input graph and dynamicallyconstruct subgraphs during the recursive subtasks, respectively. The maximalitycheck reduction minimizes the computation for ensuring maximality by utilizingneighborhood dominance between visited vertices. Extensive experiments on 18real graphs demonstrate the effectiveness of our proposed method. It achievesremarkable speedups up to 44.7x compared to existing approaches.

Accelerating Maximal Clique Enumeration via Graph Reduction