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Some efficient solutions to the affine scheduling problem -- Part I One-dimensional Time (1996)
| Citations: | 265 - 22 self |
BibTeX
@MISC{Feautrier96someefficient,
author = {Paul Feautrier},
title = {Some efficient solutions to the affine scheduling problem -- Part I One-dimensional Time},
year = {1996}
}
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Abstract
Programs and systems of recurrence equations may be represented as sets of actions which are to be executed subject to precedence constraints. In many cases, actions may be labelled by integral vectors in some iteration domain, and precedence constraints may be described by affine relations. A schedule for such a program is a function which assigns an execution date to each action. Knowledge of such a schedule allows one to estimate the intrinsic degree of parallelism of the program and to compile a parallel version for multiprocessor architectures or systolic arrays. This paper deals with the problem of finding closed form schedules as affine or piecewise affine functions of the iteration vector. An efficient algorithm is presented which reduces the scheduling problem to a parametric linear program of small size, which can be readily solved by an efficient algorithm.
Keyphrases
affine scheduling problem part one-dimensional time efficient solution efficient algorithm precedence constraint many case iteration domain affine relation recurrence equation execution date iteration vector closed form schedule piecewise affine function parallel version small size parametric linear program scheduling problem intrinsic degree multiprocessor architecture integral vector systolic array
