## Tradeoffs Between Parallelism and Fill in Nested Dissection (1999)

Citations: | 5 - 0 self |

### BibTeX

@MISC{Bornstein99tradeoffsbetween,

author = {Claudson F. Bornstein and Bruce M. Maggs and Gary L. Miller},

title = {Tradeoffs Between Parallelism and Fill in Nested Dissection},

year = {1999}

}

### OpenURL

### Abstract

In this paper we demonstrate that tradeoffs can be made between parallelism and fill in nested dissection algorithms for Gaussian elimination, both in theory and in practice. We present a new "less parallel nested dissection" algorithm (LPND), and prove that, unlike the standard nested dissection algorithm, when applied to a chordal graph LPND finds a zero-fill elimination order. We have also implemented the LPND algorithm. On a variety of benchmarks it generates less fill than state-of-the-art implementations of the nested dissection (METIS), minimum-degree (AMD), and hybrid (BEND) algorithms on a large body of test matrices. We have also implemented another nested dissection algorithm that is different from METIS and that uses the same separator algorithm used by our implementation of LPND. This algorithm, as well as LPND, generates less fill than METIS, and on large graphs significantly outperforms AMD. The latter comparison is notable, because although it is known that, for certain...