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A Massively Parallel Modularity-Maximizing Algorithm With Provable Guarantees

David Saulpic
Frederik Mallmann-Trenn
41st ACM Symposium on Principles of Distributed Computing 2022 (2022)
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Graph clustering is one of the most basic and pop- ular unsupervised learning problem. Among the different formulations of the problem, the modu- larity objective has been particularly successful for helping design impactful algorithms; Most notably the Louvain algorithm has become one of the most used algorithm for clustering graphs. Yet, one major limitation of the Louvain algorithm is its sequential nature which makes it impracti- cal in distributive environments and on massive datasets. In this paper, we provide a parallel version of Lou- vain which works in the massively parallel com- putation model (MPC). We show that it achieves optimal cluster recovery in the classic stochastic block model in only a constant number of parallel rounds, and so for the same regime of parameters than the standard Louvain algorithm as shown recently in Cohen-Addad et al. (2020).