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Abstract: The key computational step in interior-point (IP) methods for solving linear programming (LP) problems is the solution of a sparse symmetric system of linear equations (AD )\Deltay = b. The time and the memory requirements of this step depend on the initial ordering of rows and columns in the symmetric matrix AD . Computing an optimal ordering for sparse matrix factorization is an NP-complete problem and developing fast and effective ordering heuristics has been a subject of... (Update)
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BibTeX entry: (Update)
Anshul Gupta. Graph partitioning based sparse matrix ordering algorithms for interior-point methods. Technical Report RC 20467 (90480), IBM T. J. Watson Research Center, Yorktown Heights, NY, May 21, 1996. Also available at ftp://ftp.cs.umn.edu/users/kumar/anshul/IPordering. ps.Z. http://citeseer.ist.psu.edu/gupta96graph.html More
@techreport{ gupta96graph,
author = "Anshul Gupta",
title = "Graph Partitioning Based Sparse Matrix Orderings for Interior Point Algorithms",
number = "RC 20467(90480)",
year = "1996",
url = "citeseer.ist.psu.edu/gupta96graph.html" }
Citations (may not include all citations):448 A new polynomial-time algorithm for linear programming (context) - Karmarkar - 1984
429 An efficient heuristic procedure for partitioning graphs (context) - Kernighan, Lin - 1970
421 A linear time heuristic for improving network partitions (context) - Fiduccia, Mattheyses - 1982
346 Computer Solution of Large Sparse Positive Definite Systems (context) - George, Liu - 1981
288 A fast and high quality multilevel scheme for partitioning i.. - Karypis, Kumar - 1995
276 Linear Programming and Extensions (context) - Dantzig - 1963
244 A multilevel algorithm for partitioning graphs - Hendrickson, Leland - 1995
218 A separator theorem for planar graphs (context) - Lipton, Tarjan - 1979
110 Nested dissection of a regular finite-element mesh (context) - George - 1973
101 Pathways to the optimal set in linear programming (context) - Megiddo - 1989
100 Generalized nested dissection (context) - Lipton, Rose et al. - 1979
98 An approximate minimum degree ordering algorithm - Davis, Amestoy et al. - 1994
98 the implementation of a primal-dual interior point method (context) - Mehrotra - 1992
80 The evolution of the minimum degree ordering algorithm (context) - George, Liu - 1989
79 METIS: Unstructured graph partitioning and sparse matrix ord.. - Karypis, Kumar - 1995
78 A heuristic for reducing fill in sparse matrix factorization (context) - Bui, Jones - 1993
62 Computational experience with a primal-dual interior-point m.. (context) - Lustig, Marsten et al. - 1991
57 Highly scalable parallel algorithms for sparse matrix factor.. - Gupta, Karypis et al. - 1994
54 On implementing Mehrotra's predictor-corrector interior-poin.. (context) - Lustig, Marsten et al. - 1992
42 Improving the runtime and quality of nested dissection order.. - Hendrickson, Rothberg - 1996
39 Fast and effective algorithms for graph partitioning and spa.. - Gupta - 1996
36 Computing the block triangular form of a sparse matrix (context) - Pothen, Fan - 1990
34 On projected Newton barrier methods for linear programming a.. (context) - Gill, Murray et al. - 1986
32 Parallel multilevel graph partitioning - Karypis, Kumar - 1995
30 Robust ordering of sparse matrices using multisection - Ashcraft, Liu - 1996
21 Parallel formulation of interior point algorithms - Karypis, Gupta et al. - 1994
15 Communication reduction in parallel sparse Cholesky factoriz.. (context) - George, Liu et al. - 1987
10 Generalized nested dissection: Some recent progress (context) - Ashcraft, Liu - 1994
9 Sparse matrix ordering methods for interior point linear pro.. - Rothberg, Hendrickson - 1996
8 ACM Transactions on Mathematical Software (context) - Duff, Wiberg et al. - 1988
7 Parallel algorithms for forward and back substitution in dir.. - Gupta, Kumar - 1995
3 Personal Communication (context) - Rothberg - 1996
2 and sparse matrix ordering) package: Users manual (context) - Gupta, Watson - 1996
2 A parallel implementtaion of the multiple minimum degree ord.. (context) - Ghose, Rothberg - 1994
2 Publication number SC (context) - Library, Reference et al. - 1995
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