Fast Implementation of the Traveling-Salesman-Problem Method for Reordering Columns within Supernodes

In 2017 Pichon et al. introduced an effective method for reordering columns within supernodes based on reformulating the underlying optimization problem as a set of traveling salesman problems (TSP...

[1]  Joseph W. H. Liu,et al.  Modification of the minimum-degree algorithm by multiple elimination , 1985, TOMS.

[2]  J. W. Walker,et al.  Direct solutions of sparse network equations by optimally ordered triangular factorization , 1967 .

[3]  A. George.  Nested Dissection of a Regular Finite Element Mesh , 1973 .

[4]  Pierre Ramet,et al.  Reordering Strategy for Blocking Optimization in Sparse Linear Solvers , 2017, SIAM J. Matrix Anal. Appl..

[5]  Joseph W. H. Liu.  The role of elimination trees in sparse factorization , 1990 .

[6]  Cleve Ashcraft,et al.  Compressed Graphs and the Minimum Degree Algorithm , 1995, SIAM J. Sci. Comput..

[7]  Robert E. Tarjan,et al.  Three Partition Refinement Algorithms , 1987, SIAM J. Comput..

[8]  Jennifer A. Scott,et al.  Design of a Multicore Sparse Cholesky Factorization Using DAGs , 2010, SIAM J. Sci. Comput..

[9]  Timothy A. Davis,et al.  The university of Florida sparse matrix collection , 2011, TOMS.

[10]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[11]  Alan George,et al.  The Evolution of the Minimum Degree Ordering Algorithm , 1989, SIAM Rev..

[12]  D. Rose.  Triangulated graphs and the elimination process , 1970 .

[13]  Daniel J. Rosenkrantz,et al.  An Analysis of Several Heuristics for the Traveling Salesman Problem , 1977, SIAM J. Comput..

[14]  Joseph W. Liu,et al.  A compact row storage scheme for Cholesky factors using elimination trees , 1986, TOMS.

[15]  Joseph W. H. Liu,et al.  On Finding Supernodes for Sparse Matrix Computations , 1993, SIAM J. Matrix Anal. Appl..

[16]  Roger Grimes,et al.  The influence of relaxed supernode partitions on the multifrontal method , 1989, TOMS.

[17]  Barry W. Peyton,et al.  Progress in Sparse Matrix Methods for Large Linear Systems On Vector Supercomputers , 1987 .

[18]  Patrick R. Amestoy,et al.  An Approximate Minimum Degree Ordering Algorithm , 1996, SIAM J. Matrix Anal. Appl..

[19]  E. Ng,et al.  An E cient Algorithm to Compute Row andColumn Counts for Sparse Cholesky Factorization , 1994 .

[20]  A. George,et al.  On the application of the minimum degree algorithm to finite element systems , 1978 .