Engineering Data Reduction for Nested Dissection
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866910419747078144 |
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| author | Ost, Lara Schulz, Christian Strash, Darren |
| author_facet | Ost, Lara Schulz, Christian Strash, Darren |
| contents | Many applications rely on time-intensive matrix operations, such as factorization, which can be sped up significantly for large sparse matrices by interpreting the matrix as a sparse graph and computing a node ordering that minimizes the so-called fill-in. In this paper, we engineer new data reduction rules for the minimum fill-in problem, which significantly reduce the size of the graph while producing an equivalent (or near-equivalent) instance. By applying both new and existing data reduction rules exhaustively before nested dissection, we obtain improved quality and at the same time large improvements in running time on a variety of instances. Our overall algorithm outperforms the state-of-the-art significantly: it not only yields better elimination orders, but it does so significantly faster than previously possible. For example, on road networks, where nested dissection algorithms are typically used as a preprocessing step for shortest path computations, our algorithms are on average six times faster than Metis while computing orderings with less fill-in. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_11315 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Engineering Data Reduction for Nested Dissection Ost, Lara Schulz, Christian Strash, Darren Data Structures and Algorithms Combinatorics Many applications rely on time-intensive matrix operations, such as factorization, which can be sped up significantly for large sparse matrices by interpreting the matrix as a sparse graph and computing a node ordering that minimizes the so-called fill-in. In this paper, we engineer new data reduction rules for the minimum fill-in problem, which significantly reduce the size of the graph while producing an equivalent (or near-equivalent) instance. By applying both new and existing data reduction rules exhaustively before nested dissection, we obtain improved quality and at the same time large improvements in running time on a variety of instances. Our overall algorithm outperforms the state-of-the-art significantly: it not only yields better elimination orders, but it does so significantly faster than previously possible. For example, on road networks, where nested dissection algorithms are typically used as a preprocessing step for shortest path computations, our algorithms are on average six times faster than Metis while computing orderings with less fill-in. |
| title | Engineering Data Reduction for Nested Dissection |
| topic | Data Structures and Algorithms Combinatorics |
| url | https://arxiv.org/abs/2004.11315 |