Parallelization of the simplex method using the quadrant interlocking factorization
This dissertation considers the parallelization of the simplex method of linear programming. Current implementations of the simplex method on sequential computers are based on a triangular factorization of the inverse of the current basis. An alternative decomposition designed for parallel computation, called the quadrant interlocking factorization, has previously been proposed for solving linear systems of equations. This research presents the theoretical justification and algorithms required to implement this new factorization in a simplex-based linear-programming system. Four algorithms are presented for updating the quadrant-interlocking factorization of the basis matrix when modified by a rank-one matrix. Parallel algorithms for producing the factorization in product form and for solving the linear systems of the simplex method are developed. The computations are scheduled to minimize the total execution time on a multiple-instructions multiple-data (MIMD) parallel computer that incorporates p identical processors sharing a common memory.
- Research Organization:
- Southern Methodist Univ., Dallas, TX (USA)
- OSTI ID:
- 5221666
- Country of Publication:
- United States
- Language:
- English
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