A Convex-Programming Approach for Efficient Directed Densest Subgraph Discovery

Given a directed graph G, the directed densest subgraph (DDS) problem refers to finding a subgraph from G, whose density is the highest among all subgraphs of G. The DDS problem is fundamental to a wide range of applications, such as fake follower detection and community mining. Theoretically, the DDS problem closely connects to other essential graph problems, such as network flow and bipartite matching. However, existing DDS solutions suffer from efficiency and scalability issues. In this paper, we develop a convex-programming-based solution by transforming the DDS problem into a set of linear programs. Based on the duality of linear programs, we develop efficient exact and approximation algorithms. Especially, our approximation algorithm can support flexible parameterized approximation guarantees. We have performed an extensive empirical evaluation of our approaches on eight real large datasets. The results show that our proposed algorithms are up to five orders of magnitude faster than the state-of-the-art.