On the complexity of task graph scheduling with transient and fail-stop failures

This paper deals with the complexity of task graph scheduling with transient and fail-stop failures. While computing the reliability of a given schedule is easy in the absence of task replication, the problem becomes much more difficult when task replication is used. Our main result is that this problem is #P’Complete (hence at least as hard as NP-Complete problems), with both transient and fails-stop processor failures. We also study the complexity of a restricted class of schedules, where a task cannot be scheduled before all replicas of all its predecessors have completed their execution.