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The parallel ordering of large graphs is a difficult problem, because on theone hand minimum degree algorithms do not parallelize well, and on the otherhand the obtainment of high quality orderings with the nested dissectionalgorithm requires efficient graph bipartitioning heuristics, the bestsequential implementations of which are also hard to parallelize. This paperpresents a set of algorithms, implemented in the PT-Scotch software package,which allows one to order large graphs in parallel, yielding orderings thequality of which is only slightly worse than the one of state-of-the-artsequential algorithms. Our implementation uses the classical nested dissectionapproach but relies on several novel features to solve the parallel graphbipartitioning problem. Thanks to these improvements, PT-Scotch producesconsistently better orderings than ParMeTiS on large numbers of processors.

PT-Scotch: A tool for efficient parallel graph ordering