Direct methods for sparse matrices
Direct methods for sparse matrices
Computing the block triangular form of a sparse matrix
ACM Transactions on Mathematical Software (TOMS)
Finding good approximate vertex and edge partitions is NP-hard
Information Processing Letters
Partitioning Rectangular and Structurally Unsymmetric Sparse Matrices for Parallel Processing
SIAM Journal on Scientific Computing
Preconditioning Highly Indefinite and Nonsymmetric Matrices
SIAM Journal on Scientific Computing
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
Reducing the Total Bandwidth of a Sparse Unsymmetric Matrix
SIAM Journal on Matrix Analysis and Applications
On Two-Dimensional Sparse Matrix Partitioning: Models, Methods, and a Recipe
SIAM Journal on Scientific Computing
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We consider the following problem: given a square, nonsymmetric, (0, 1)-matrix, find a permutation of its columns that yields a zero-free diagonal and maximizes the symmetry. The problem is known to be NP-hard. We propose a fast iterative-improvement based heuristic and evaluate the performance of the heuristic on a large set of matrices.