Abstract
Graph partitioning is a fundamental problem in several scientific and engineering applications, including task partitioning for parallel processing. In this paper, we describe heuristics that improve the state-of-the-art practical algorithms used in graph partitioning software in terms of both partitioning speed and quality. An important use of graph partitioning is in ordering sparse matrices for obtaining direct solutions to sparse systems of linear equations arising in engineering and optimization applications. The experiments reported in this paper show that the use of these heuristics results in a considerable improvement in the quality of sparse matrix orderings over conventional ordering methods. In addition, our graph-partitioning based ordering algorithm is more parallelizable than minimum-degree based orderings algorithms and it renders the ordered matrix more amenable to parallel factorization.
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Gupta, A., Gustavson, F. (1996). First graph partitioning and its application in sparse matrix ordering. In: Waśniewski, J., Dongarra, J., Madsen, K., Olesen, D. (eds) Applied Parallel Computing Industrial Computation and Optimization. PARA 1996. Lecture Notes in Computer Science, vol 1184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62095-8_34
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DOI: https://doi.org/10.1007/3-540-62095-8_34
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