Scalable stochastic block partition

Abstract

The processing of graph data at large scale, though important and useful for real-world applications, continues to be challenging, particularly for problems such as graph partitioning. Optimal graph partitioning is NP-hard, but several methods provide approximate solutions in reasonable time. Yet scaling these approximate algorithms is also challenging. In this paper, we describe our efforts towards improving the scalability of one such technique, stochastic block partition, which is the baseline algorithm for the IEEE HPEC Graph Challenge [1]. Our key contributions are: improvements to the parallelization of the baseline bottom-up algorithm, especially the Markov Chain Monte Carlo (MCMC) nodal updates for Bayesian inference; a new top-down divide and conquer algorithm capable of reducing the algorithmic complexity of static partitioning and also suitable for streaming partitioning; a parallel single-node multi-CPU implementation and a parallel multi-node MPI implementation. Although our focus is on algorithmic scalability, our Python implementation obtains a speedup of 1.65× over the fastest baseline parallel C++ run at a graph size of 100k vertices divided into 8 subgraphs on a multi-CPU single node machine. It achieves a speedup of 61× over itself on a cluster of 4 machines with 256 CPUs for a 20k node graph divided into 4 subgraphs, and 441× speedup over itself on a 50k node graph divided into 8 subgraphs on a multi-CPU single node machine.