Scheduling of Parallel Programs in Single-Bus Multiprocessor Systems

Consider a scheduling problem of parallel computations in multiproces-sor systems. Let a parallel program be represented by a task graph, where vertices represent tasks and arcs represent the communications between the tasks. An in-terprocessor communication time incurs when two tasks assigned to two diierent processors have to communicate. Such a scheduling problem has recently been studied in the literature, mostly for the case where interprocessor communication times are fully determined. In this paper, we consider the scheduling problem with resource constraints. More speciically, we consider the case where all interprocessor communications take place on a single bus. We show that even for very speciic sub-problems, the minimization of the makespan of parallel programs in such a single-bus multiprocessor system is NP-hard. Thus, the general scheduling problem of parallel programs with communication resource constraints is NP-hard. We consider several variants of the problem: tasks with or without preallocation, communications with independent-data semantics or common-data semantics. Our results are extended to the cases of blocking communications and of broadcasting communications, and can be applied to multiprocessor systems with shared memory. Ordonnancement de programmes parall eles sur des machines multiprocesseurs a bus unique R esum e : Nous consid erons un probl eme d'ordonnancement pour les calculs pa-rall eles dans un syst eme multiprocesseur. Un programme parall ele est repr esent e par un graphe de t^ aches, o u les sommets repr esentent les t^ aches et les arcs les communications entre les t^ aches. Un tel probl eme a et e r ecemment etudi e dans la litt erature dans le cas o u les temps de communication ne d ependent pas de l' etat du syst eme. Dans cet article, nous consid erons le probl eme d'ordonnancement avec contrainte de ressources. Plus pr ecisement, nous etudions le cas o u toutes les communications ont lieu sur un bus unique. Nous prouvons que, m^ eme pour des sous-probl emes sp eci-ques, la minimisation de la dur ee d'ordonnancement pour les programmes parall eles dans un tel syst eme multiprocesseur est NP-diicile. Cela implique que le probl eme g en eral d'ordonnancement pour les programmes parall eles avec des contraintes des ressources de communication est NP-diicile. Nous analysons plusieurs variantes du probl eme : les t^ aches avec ou sans allocation au pr ealable, les communications avec s emantique de donn ees ind ependantes ou s emantique de donn ees communes. Nos …