M Yannanakis. Computing the minimum fill-in is NP-complete. SIAM Journal of Algebraic and Discrete Methods, 1981. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Generic Graph Algorithms for Sparse Matrix Ordering - Lee, Siek, Lumsdaine (1999) (2 citations) (Correct)
....numerical pivoting) of symmetric positive definite systems is stable, such systems can be ordered before factorization takes place based only on the structure of the sparse matrix. Unfortunately, determining the optimal ordering (in the sense of minimizing fill in) is an NP complete problem [1], so greedy heuristic algorithms are typically used instead. The development of algorithms for sparse matrix ordering has been an active research topic for many years. The algorithms are typically developed in graph theoretical terms, while the most widely used implementations are coded in ....
....non zero structure of L that are not present in the nonzero structure of A) the ordering has a significant impact on the memory and computational requirements for the latter stages. However, finding the optimal ordering for A (in the sense of minimizing fill in) has been proven to be NP complete [1] requiring that heuristics be used for all but simple (or specially structured) cases. Developing algorithms for high quality orderings has been an active research topic for many years. Most ordering algorithms in wide use are based on a greedy approach such that the ordering is chosen to ....
M Yannanakis. Computing the minimum fill-in is NP-complete. SIAM Journal of Algebraic and Discrete Methods, 1981.
The High Performance Generic Graph Component Library - Lee (1999) (Correct)
....non zero structure of L that are not present in the non zero structure of A) the ordering has a significant impact on the memory and computational requirements for the latter stages. However, finding the optimal ordering for A (in the sense of minimizing fill in) has been proven to be NP complete [29] requiring that heuristics be used for all but simple (or specially structured) cases. An widely used but rather simple ordering algorithm is a variant of the Cuthill McKee orderings. It also can be used as a preordering method to improve ordering in more sophisticated methods such as minimum ....
M. Yannanakis. Computing the minimum fill-in is NP-complete. SIAM Journal of Algebraic and Discrete Methods, 1981.
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