A Parallel Solver for Graph Laplacians

Problems from graph drawing, spectral clustering, network flow and graph parti- tioning all can be expressed as Laplacian matrices. Theoretically fast approaches to solving these problems exist, but in practice these techniques are slow. Three practical approaches have been proposed and work well in serial. However, as problem sizes increase and single core speeds stagnate, parallelism is essential to solve problems quickly. We present an unsmoothed aggregation Multigrid method for solving graph Laplacians in distributed memory setting. Our solver scales up to 64 compute nodes and achieves speedups of up to 83x over the existing serial solutions.