Improved Online Scheduling with Restarts on a Single Machine

Abstract We consider the problem of minimizing the total completion time on a single online machine using 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. We present a very simple online algorithm which is better than 1.4568-competitive. The basic rule of the algorithm is to run jobs in order of increasing size. For possible restarts, the algorithm only considers whether the completion time of an incoming job is more than a factor of 1.4568 higher if we first let the running job finish compared to the case where we start the new job immediately. If this is the case, we interrupt the running job and start running the new job. All other existing or past jobs are ignored for this decision. The analysis of the algorithm has become significantly easier and shorter than for the previous best result which was 3/2. We hope that this result can lead to further research in this interesting topic.