New Parallel and Streaming Algorithms for Directed Densest Subgraph
Slobodan Mitrovic, Theodore Pan, Mahdi Qaempanah, Mohammad Amin Raeisi
Finding dense subgraphs is a fundamental problem with applications to community detection, clustering, and data mining. Our work focuses on finding approximate densest subgraphs in directed graphs in computational models for processing massive data. We consider two such models: Massively Parallel Computation (MPC) and semi-streaming. We show how to find a $(2+\varepsilon)$-approximation in $\tilde{O}(\sqrt{\log n})$ MPC rounds with sublinear memory per machine. This improves the state-of-the-art results by Bahmani et al. (WAW 2014) and Mitrovic \& Pan (ICML 2024). Moreover, we show how to find an $O(\log n)$-approximation in a single pass in semi-streaming. This is in stark contrast to prior work, which implies $\tilde{\Omega}(n^{1/6})$-approximation for a single pass; a better approximation is known only for randomized streams (Mitrovi\'c \& Pan). We empirically evaluate our approaches in two ways. First, we illustrate that our single-pass semi-streaming algorithm performs much better than the theoretical guarantee. Specifically, its approximation on temporal datasets matches the $(2+\varepsilon)$-approximation of an $O(\log n)$-pass algorithm by Bahmani et al. (VLDB 2012). Second, we demonstrate that our MPC algorithm requires fewer rounds than prior work.