Schedules with a single preemption on uniform parallel machines

For a scheduling problem to minimize the makespan on parallel machines, we consider schedules with at most one preemption. We show that in the case of two uniform machines the problem is solvable in polynomial time. For m≥3 uniform parallel machines, we measure the quality of a single preemption as the worst-case ratio of the makespan of an optimal schedule with at most one preemption over the makespan of an optimal preemptive schedule. We show that the global bound on such a ratio is 2−2∕m.