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This paper presents a novel meta algorithm, Partition-Merge (PM), which takesexisting centralized algorithms for graph computation and makes themdistributed and faster. In a nutshell, PM divides the graph into smallsubgraphs using our novel randomized partitioning scheme, runs the centralizedalgorithm on each partition separately, and then stitches the resultingsolutions to produce a global solution. We demonstrate the efficiency of the PMalgorithm on two popular problems: computation of Maximum A Posteriori (MAP)assignment in an arbitrary pairwise Markov Random Field (MRF), and modularityoptimization for community detection. We show that the resulting distributedalgorithms for these problems essentially run in time linear in the number ofnodes in the graph, and perform as well -- or even better -- than the originalcentralized algorithm as long as the graph has geometric structures. Here wesay a graph has geometric structures, or polynomial growth property, when thenumber of nodes within distance r of any given node grows no faster than apolynomial function of r. More precisely, if the centralized algorithm is aC-factor approximation with constant C \ge 1, the resulting distributedalgorithm is a (C+\delta)-factor approximation for any small \delta>0; but ifthe centralized algorithm is a non-constant (e.g. logarithmic) factorapproximation, then the resulting distributed algorithm becomes a constantfactor approximation. For general graphs, we compute explicit bounds on theloss of performance of the resulting distributed algorithm with respect to thecentralized algorithm.

Partition-Merge: Distributed Inference and Modularity Optimization