We empirically study state-of-the-art parallel graph partitioning and sparse matrix ordering software packages. We compare their speed, quality, and robustness. For a model case, in which good partitionings (even optimal partitionings, in some cases) can be constructed manually, we compare the size of the edge cuts of the manual partitions with that of the partitions generated by the multilevel heuristics that are at the heart of modern graph partitioning software packages. We show that the quality of the partitions generated by the software is only slightly worse than that of the manual partition for this class of model graphs. We discuss the shortcomings of the current ordering software and argue that there is an urgent need for more robust, scalable, and high-quality software for sparse matrix ordering to support scalable solution of sparse linear systems by direct methods on massively parallel computers.
By: Anshul Gupta
Published in: RC25008 in 2010
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