On optimal fill-preserving orderings of sparse matrices for parallel Cholesky factorizations

Wen-Yang Lin, Chuen-Liang Chen
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引用次数: 1

Abstract

In this paper, we consider the problem of finding fill-preserving ordering of a sparse symmetric and positive definite matrix such that the reordered matrix is suitable for parallel factorization. We extended the unit-cost fill-preserving ordering into a generalized class that can adopt various aspects in parallel factorization, such as computation, communication and algorithmic diversity. Based on the elimination tree model, we show that as long as the node cost function for factoring a column/row satisfies two mandatory properties, we can deploy a greedy-based algorithm to find the corresponding optimal ordering. The complexity of our algorithm is O(q log q+/spl kappa/), where q denotes the number of maximal cliques, and /spl kappa/ the sum of all maximal clique sizes in the filled graph. Our experiments reveal that on the average, our minimum completion cost ordering (MinCP) would reduce up to 17% the cost to factor than minimum height ordering (Jess-Kees).
并行Cholesky分解稀疏矩阵的最优保填充排序
本文研究了一个稀疏对称正定矩阵的保填充排序问题,使得该重排序矩阵适合于并行分解。我们将单位成本保补排序推广为一个广义类,它可以在并行分解中采用计算、通信和算法多样性等方面。基于消去树模型,我们证明了只要分解列/行的节点代价函数满足两个强制属性,我们就可以部署基于贪婪的算法来找到相应的最优排序。算法的复杂度为O(q log q+/spl kappa/),其中q表示最大团的个数,/spl kappa/表示填充图中所有最大团的大小之和。我们的实验表明,平均而言,我们的最小完井成本排序(MinCP)将比最小高度排序(jesse - kees)减少高达17%的因子成本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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