The Impact of Restarts in Online Machine Scheduling

This dissertation investigates the impact of job preemptions and restarts in online machine scheduling, with a focus on three fundamental objectives. An online scheduling algorithm determines whether to process a job or not without knowing the future events. One important extension to the classical online scheduling framework is the use of restarts. Allowing restarts means that the processing of a job may be interrupted, but in this case the interrupted job loses all its previous progress and must be started again later, until it is completed without interruptions. This model also known as preemption with restarts. Although restarts can potentially be very beneficial in the context of online scheduling, there has been relatively little research on this topic up until now.

First, we study the problem of minimizing the total completion time on a single machine. We present a simple deterministic online algorithm that achieves a competitive ratio better than 1.4568, improving upon the previous best bound of 3/2. The algorithm follows an increasing-size processing order and interrupts a running job only when doing so reduces the completion time of an arriving job by more than a factor of 1.4568 compared to processing it immediately.

Second, we extend the results to the minimization of total weighted completion time. For the case of equal processing times, we design a deterministic online algorithm that achieves a competitive ratio better than 1.325 based on carefully structured decision intervals. The algorithm uses at most three restarts for the entire schedule and redefines these decision intervals in certain situations to avoid further interruptions.

Finally, we consider the weighted makespan minimization problem. This problem is generalization of the classical makespan minimization problem. We present a deterministic online algorithm that achieves a competitive ratio better than 1.3098 in the case where all jobs have equal processing times.