PROCESSOR LOWER BOUND FORMULAS FOR ARRAY COMPUTATIONS AND PARAMETRIC DIOPHANTINE SYSTEMS

PETER CAPPELLO, ÖMER EĞECIOĞLU
1998 International Journal of Foundations of Computer Science  
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 d n to a set of parametric
more » ... Diophantine equations. We illustrate an algorithm based on generating functions for constructing a formula for these numbers d n . 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.
doi:10.1142/s0129054198000295 fatcat:ic2n4sbstjeb7aezglob5gastq