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IPPS

1998

IEEE

1998

IEEE

Using a directed acyclic graph (dag) model of algorithms, we solve a problem related to precedenceconstrained multiprocessor schedules for array computations: Given a sequence of dags and linear schedules parametrized by n, compute a lower bound on the number of processors required by the schedule as a function of n. In our formulation, the number of tasks that are scheduled for execution during any fixed time step is the number of non-negative integer solutions dn to a set of parametric linear Diophantine equations. We illustrate an algorithm based on generating functions for constructing a formula for these numbers dn. The algorithm has been implemented as a Mathematica program. An example run and the symbolic formula for processor lower bounds automatically produced by the algorithm for Gaussian Elimination is presented.

Added |
05 Aug 2010 |

Updated |
05 Aug 2010 |

Type |
Conference |

Year |
1998 |

Where |
IPPS |

Authors |
Peter R. Cappello, Ömer Egecioglu |

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