Scalable Algorithms for Densest Subgraph Discovery.

As a fundamental problem in graph data mining, Densest Subgraph Discovery (DSD) aims to find the subgraph with the highest density from a graph. It has been studied for several decades and found a large number of real-world applications, such as network community detection, regulatory motif discovery in DNA, graph index construction, and fake follower detection. Although there are many existing DSD algorithms, they are often not scalable or efficient to process large-scale graphs, since most of them are serial algorithms and can only leverage the computing resource of a single CPU core. To tackle these issues, in this paper we propose efficient parallel algorithms for solving the DSD problems on both undirected and directed graphs at scale. Our main idea is to use the k-cores (a kind of dense subgraph) to approximate the densest subgraph in the undirected graphs, and then propose efficient parallel algorithms for computing the cores by optimizing the iterative process and also reducing the number of iterations. We further extend this idea for directed graphs by introducing a novel concept, named w-induced subgraph, to avoid unnecessary enumerations of x or y when searching [x,y]-cores (a kind of directed dense subgraph to approximate the densest). To verify the scalability and efficiency of the proposed algorithms, we have conducted extensive experiments on 12 large real-world graphs, and four of them are billion-scale. The experimental results show that our proposed algorithms outperform the state-of-the-art algorithms on both undirected and directed graphs, in terms of scalability and efficiency.