UC Santa Cruz

Reducing communication is an important objective, as it can save energy or improve the performance of a communication-bound application. The graph algorithm PageRank computes the importance of vertices in a graph, and it serves as an important benchmark for graph algorithm performance. If the input graph to PageRank has poor locality, the execution will need to read many cache lines from memory, some of which may not be fully utilized. We present propagation blocking, an optimization to improve spatial locality, and we demonstrate its application to PageRank. In contrast to cache blocking which partitions the graph, we partition the data transfers between vertices (propagations). If the input graph has poor locality, our approach will reduce communication. Our approach reduces communication more than conventional cache blocking if the input graph is sufficiently sparse or if number of vertices is sufficiently large relative to the cache size. To evaluate our approach, we use both simple analytic models to gain insights and precise hardware performance counter measurements to compare implementations on a suite of 8 real-world and synthetic graphs. We demonstrate our parallel implementations substantially outperform prior work in execution time and communication volume. Although we present results for PageRank, propagation blocking could be generalized to SpMV (sparse matrix multiplying dense vector) or other graph programming models.