A Scalability and Sensitivity Study of Parallel Geometric Algorithms for Graph Partitioning

Abstract

Graph partitioning arises in many computational simulation workloads, including those that involve finite difference or finite element methods, where partitioning enables efficient parallel processing of the entire simulation. We focus on parallel geometric algorithms for partitioning large graphs whose vertices are associated with coordinates in two or three-dimensional space on multi-core processors. Compared with other types of partitioning algorithms, geometric schemes generally show better scalability on a large number of processors or cores. This paper studies the scalability and sensitivity of two parallel algorithms, namely, recursive coordinate bisection (denoted by pRCB) and geometric mesh partitioning (denoted by pGMP), in terms of their robustness to several key factors that affect the partition quality, including coordinate perturbation, approximate embedding, mesh quality and graph planarity. Our results indicate that the quality of a partition as measured by the size of the edge separator (or cutsize) remains consistently better for pGMP compared to pRCB. On average for our test suite, relative to pRCB, pGMP yields 25% smaller cutsizes on the original embedding, and across all perturbations cutsizes that are smaller by at least 8% and by as much as 50%. Not surprisingly, higher quality cuts are obtained at the expense of longer execution times; on a single core, pGMP has an average execution time that is almost 10 times slower than that of pRCB, but it scales better and catches up at 32-cores to be slower by less than 20%. With the current trends in core counts that continue to increase per chip, these results suggest that pGMP presents an attractive solution if a modest number of cores can be deployed to reduce execution times while providing high quality partitions.