Distributed Graph Clustering and Sparsification

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of algorithmic design methods for graph clustering. Most of these methods, however, are based on complicated spectral techniques or convex optimisation, and cannot be directly applied for clustering many networks that occur in practice, whose information is often collected on different sites. Designing a simple and distributed clustering algorithm is of great interest, and has wide applications for processing big datasets. In this paper we present a simple and distributed algorithm for graph clustering: for a wide class of graphs that are characterised by a strong cluster-structure, our algorithm finishes in a poly-logarithmic number of rounds, and recovers a partition of the graph close to optimal. One of the main components behind our algorithm is a sampling scheme that, given a dense graph as input, produces a sparse subgraph that provably preserves the cluster-structure of the input. Compared with previous sparsification algorithms that require Laplacian solvers or involve combinatorial constructions, this component is easy to implement in a distributed way and runs fast in practice.