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ISPAN
2002
IEEE

Automatic Processor Lower Bound Formulas for Array Computations

13 years 7 months ago
Automatic Processor Lower Bound Formulas for Array Computations
In the directed acyclic graph (dag) model of algorithms, consider the following problem for precedence-constrained multiprocessor schedules for array computations: Given a sequence of dags and linear schedules parameterized by Ò, compute a lower bound on the number of processors required by the schedule as a function of Ò. This problem is formulated so that the number of tasks that are scheduled for execution during any fixed time step is the number of non-negative integer solutions Ò to a set of parametric linear Diophantine equations. Generating function methods are then used for constructing a formula for the numbers Ò. We implemented this algorithm as a Mathematica program. This paper is an overview of the techniques involved and their applications to well-known schedules for MatrixVector Product, Triangular Matrix Product, and Gaussian Elimination dags. Some example runs and automatically produced symbolic formulas for processor lower bounds by the algorithm are given.
Peter R. Cappello, Ömer Egecioglu
Added 15 Jul 2010
Updated 15 Jul 2010
Type Conference
Year 2002
Where ISPAN
Authors Peter R. Cappello, Ömer Egecioglu
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