Communication-efficient Massively Distributed Connected Components

Finding the connected components of an undirected graph is one of the most fundamental graph problems. Connected components are used in a wide spectrum of applications including VLSI design, machine learning and image analysis. Sequentially, one can easily find all connected components in linear time using breadth-first traversal. However, in a massively distributed setting, finding connected components in a scalable way becomes much harder due to data irregularities and the overhead associated with the increased need for communication. In this work, we present a communication-efficient distributed graph algorithm for finding connected components that scales to massively parallel machines. Our algorithm is based on a recent linear-work shared-memory parallel algorithm by Blelloch et al. [1] and refines it for a distributed memory setting. This includes a communication-efficient graph contraction procedure, as well as a distributed variant of the low diameter decomposition by Miller et al. [2]. We tackle the data irregularities introduced by high degree vertices by using an efficient procedure for distributing their incident edges. Our experimental evaluation on up to 16384 cores indicates a good weak scaling behavior that outperforms current state-of-the-art algorithms.