The Parallel Evaluation of General Arithmetic Expressions
Journal of the ACM (JACM)
A Survey of Parallel Machine Organization and Programming
ACM Computing Surveys (CSUR)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Parallel Algorithms to Set Up the Benes Permutation Network
IEEE Transactions on Computers
A Data Structure for Parallel L/U Decomposition
IEEE Transactions on Computers
A Computation Model of Parallel Solution of Linear Equations
IEEE Transactions on Computers
Optimal Scheduling Strategies in a Multiprocessor System
IEEE Transactions on Computers
An optimal schedule for Gaussian elimination on an MIMD architecture
Journal of Computational and Applied Mathematics
| Hi-index | 14.98 |
A parallel algorithm for Gaussian elimination (GE) is described, which solves a linear system of size n using m = n parallel processors and a shared random access memory. Converting the serial GE algorithm to parallel form involves scheduling its computation DAG (directed acyclic graph) on m processors. A lower bound for schedule length is established for dense GE DAG's and it is proved that the proposed algorithm produces schedules which achieve these bounds. Finally, both the construction and execution of the schedule are incorporated into a single concurrent program which is shown to run in optimal time.