Complexity of Scheduling Tasks with Time-Dependent Execution Times

Abstract A new model of task system in which the execution time of a task depends on its starting time is considered. It is shown that the feasibility problem on a single processor is NP-complete for a set of tasks with identical release times and two distinct deadlines. An O(n log n)-time algorithm is given for a set of tasks with identical release times and deadlines. These two results give a sharp boundary delineating the complexity of the problem.