i S pan : Parallel Identification of Strongly Connected Components with Spanning Trees

Abstract

Detecting strongly connected components (SCCs) in a directed graph is crucial for understanding the structure of graphs. Most real-world graphs have one large SCC that contains the majority of the vertices as well as many small SCCs whose sizes are reversely proportional to the frequency of their occurrences. For both types of SCCs, current approaches that rely on depth first search (DFS) or breadth first search (BFS) face the challenges of both strict synchronization requirements and high computation cost. In this article, we advocate a new paradigm of identifying SCCs with simple spanning trees since SCC detection requires only the knowledge of connectivity among the vertices. We have developed a prototype called i S pan , which consists of parallel, relaxed synchronization construction of spanning trees for detecting large and small SCCs combined with fast trims for small SCCs. We further scale i S pan to the distributed memory system by applying different distribution strategies to the data and task parallel jobs. Not limited, we also extend i S pan to the GPU architecture. The evaluations show that i S pan is able to significantly outperform current state-of-the-art DFS- and BFS-based methods by an average 18× and 4×, respectively.