Scheduling Tasks with AND/OR Precedence Constraints

Abstract

In traditional precedence-constrained scheduling a task is ready to execute when all its predecessors are complete. We call such a task an AND task. In this paper we allow certain tasks to be ready when just one of their predecessors is complete. These tasks are known as OR tasks. We analyze the complexity of two types of real-time AND/OR task scheduling problems. In the first type of problem, all the predecessors of every OR task must eventually be completed, but in the second type of problem, some OR predecessors may be left unscheduled. We show that most problems involving tasks with individual deadlines are NP-complete, and then present two priority-driven heuristic algorithms to minimize completion time on a multiprocessor. These algorithms provide the same level of worst-case performance as some previous priority-driven algorithms for scheduling AND-only task systems.