Revisiting dynamic DAG scheduling under memory constraints for shared-memory platforms
Abstract
This work focuses on dynamic DAG scheduling under memory constraints.We target a shared-memory platform equipped with p parallel processors. We aim at bounding the maximum amount of memory that may be needed by any schedule using p processors to execute the DAG. We refine the classical model that computes maximum cuts by introducing two types of memory edges in the DAG, black edges for regular precedence constraints and red edges for actual memory consumption during execution. A valid edge cut cannot include more thanpred edges. This limitation had never been taken intoaccount in previous works, and dramatically changes the complexity of the problem, which was polynomial and becomes NP-hard. We introduce an Integer Linear Program (ILP) to solve it, together with an efficient heuristic based on rounding the rational solution ofthe ILP. In addition, we propose an exact polynomial algorithm for series-parallel graphs. We provide an extensive set of experiments, both with randomly-generated graphs and with graphs arising form practical applications, which demonstrate the impact of resource constraints on peak memory usage
Nous étudions l’ordonnancement de graphes de tâches sous contrainte mémoire, et proposons un nouveau modèle qui prend en compte le caractère limité des ressources. Nous montrons que déterminer la ressource mémoire maximale nécessaire à tout ordonnancement dynamique devient un problème NP-complet,. Nous proposons un programme linéaire en nombre sentiers et une heuristique pour le résoudre. Nous conduisons un ensemble de simulations sur des graphes aléatoires ou issus d’applications, et démontrons tout l’impact de la limitation de ressources sur la consommation mémoire maximale
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