Tradeoffs between parallelism and fill in nested dissection
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
An Object-Oriented Collection of Minimum Degree Algorithms
ISCOPE '98 Proceedings of the Second International Symposium on Computing in Object-Oriented Parallel Environments
Impact of reordering on the memory of a multifrontal solver
Parallel Computing - Parallel matrix algorithms and applications (PMAA '02)
Adapting a parallel sparse direct solver to architectures with clusters of SMPs
Parallel Computing - Special issue: Parallel and distributed scientific and engineering computing
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
A column approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Algorithm 837: AMD, an approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
A robust ILU preconditioner using constraints diagonal Markowitz
Proceedings of the 48th Annual Southeast Regional Conference
| Hi-index | 0.00 |
The minimum degree and minimum local fill algorithms are two bottom-up heuristics for reordering a sparse matrix prior to factorization. Minimum degree chooses a node of least degree to eliminate next; minimum local fill chooses a n ode whose elimination creates the least fill. Contrary to popular belief, we find that minimum local fill produces significantly better orderings than minimum degree, albeit at a greatly increased runtime. We describe two simple modifications to this strategy that further improve ordering quality. We also describe a simple modification to minimum degree, which we term approximate minimum mean local fill, that reduces factorization work by roughly 25% with only a small increase in runtime.