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arXiv · 1105.4490

A Geometric Approach to Matrix Ordering

B. O. Fagginger Auer·R. H. Bisseling
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Abstract

We present a recursive way to partition hypergraphs which creates and exploits hypergraph geometry and is suitable for many-core parallel architectures. Such partitionings are then used to bring sparse matrices in a recursive Bordered Block Diagonal form (for processor-oblivious parallel LU decomposition) or recursive Separated Block Diagonal form (for cache-oblivious sparse matrix-vector multiplication). We show that the quality of the obtained partitionings and orderings is competitive by comparing obtained fill-in for LU decomposition with SuperLU (with better results for 8 of the 28 test matrices) and comparing cut sizes for sparse matrix-vector multiplication with Mondriaan (with better results for 4 of the 12 test matrices). The main advantage of the new method is its speed: it is on average 21.6 times faster than Mondriaan.

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B. O. Fagginger Auer, R. H. Bisseling. 2011-05-23. A Geometric Approach to Matrix Ordering. https://arxiv.org/abs/1105.4490

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