A new polynomial-time algorithm for linear programming
Combinatorica
Direct methods for sparse matrices
Direct methods for sparse matrices
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Equivalent sparse matrix reordering by elimination tree rotations
SIAM Journal on Scientific and Statistical Computing
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Hypercube implementation of the simplex algorithm
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
A graph partitioning algorithm by node separators
ACM Transactions on Mathematical Software (TOMS)
The minimum degree ordering with constraints
SIAM Journal on Scientific and Statistical Computing
Linear programming and network flows (2nd ed.)
Linear programming and network flows (2nd ed.)
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
Parallel algorithms for sparse linear systems
SIAM Review
Linear optimization and extensions: theory and algorithms
Linear optimization and extensions: theory and algorithms
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Fast and effective algorithms for graph partitioning and sparse-matrix ordering
IBM Journal of Research and Development - Special issue: optical lithography I
Highly Scalable Parallel Algorithms for Sparse Matrix Factorization
IEEE Transactions on Parallel and Distributed Systems
A scalable parallel algorithm for sparse Cholesky factorization
Proceedings of the 1994 ACM/IEEE conference on Supercomputing
Nonlinear optimization and parallel computing
Parallel Computing - Special issue: Parallel computing in numerical optimization
Scaling performance of interior-point method on large-scale chip multiprocessor system
Proceedings of the 2007 ACM/IEEE conference on Supercomputing
Parallel Implementation of Generalized Newton Method for Solving Large-Scale LP Problems
PaCT '09 Proceedings of the 10th International Conference on Parallel Computing Technologies
Gigaflops in linear programming
Operations Research Letters
| Hi-index | 0.00 |
In this paper we describe a scalable parallel formulation of interior point algorithms. Through our implementation on a 256-processor nCUBE 2 parallel computer, we show that our parallel formulation utilizes hundreds of processors efficiently and delivers much higher performance and speedups than reported earlier. These speedups are a result of our highly efficient parallel algorithm for solving a linear symmetric positive definite system using Cholesky factorization. We also evaluate a number of ordering algorithms for sparse matrix factorization in terms of their suitability for parallel Cholesky factorization.