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Proceedings
2021 Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX)

Engineering Data Reduction for Nested Dissection

Abstract

Many applications rely on solving sparse linear systems, which can be sped up significantly by permuting the matrix to minimize the number of non-zeros introduced by factorization—the fill-in. Equivalently, one can compute an elimination order of the graph that minimizes the number of introduced edges, for which the fast but inexact nested dissection algorithm is often used in practice. 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. 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.

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cover image Proceedings
2021 Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX)
Pages: 113 - 127
Editors: Farach-Colton Martin and Storandt Sabine
ISBN (Online): 978-1-61197-647-2

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Published online: 7 January 2021

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