Profile Scheduling by List Algorithms

The notion of proole scheduling was rst introduced by Ullman in 1975 in the complexity analysis of deterministic scheduling algorithms. In such a model, the number of processors available to a set of tasks may vary in time. Since the last decade, this model has been used to deal with systems subject to processor failures, multipro-grammed systems, or dynamically reconngured systems. The aim of this paper is to overview optimal polynomial solutions for scheduling a set of partially ordered tasks in these systems. Particular attentions are given to a class of algorithms referred to as list scheduling algorithms. The objective of the scheduling problem is to minimize either the maximum lateness or the makespan. Results on preemptive and nonpreemptive deterministic scheduling, and on preemptive stochastic scheduling, are presented. Consider the problem of scheduling a set of partially ordered tasks represented by a directed acyclic graph, referred to as task graph, where vertices represent tasks and arcs represent precedence relations. Tasks are executed, subject to precedence constraints, on a set of parallel identical processors. The number of available processors, referred to as proole, may vary in time. Task and processor assignments must be nonredundant, at any time, a task can be assigned to at most one processor, and a processor can execute at most one task. Each task has a due date. The objective is to minimize the maximum lateness or, when due dates are not taken into consideration, the makespan. The notion of proole scheduling was rst introduced by Ullman 31] and later used by Garey et al. 15] in the complexity analysis of deterministic scheduling algorithms. In this paper we use the notion of proole to deal with systems subject to processor failures , multiprogrammed systems, or dynamically reconngured systems. In such cases, the number of processors available to a set of tasks may vary in time. The problem of minimizing the maximum lateness and the makespan is in general NP-hard. We are interested in simple on-line or nearly on-line algorithms which yield optimal solutions under speciic assumptions. Results on three problems will be presented here, with each result accounting for diierent task characteristics. The reader is referred to the survey paper by Lawler et al. 20] for results on optimal scheduling under a constant proole, i.e., when the number of available processors is constant. The rst results on optimal polynomial solutions for proole scheduling problems are due to …