On-line scheduling on a single machine: Maximizing the number of early jobs

This note deals with the scheduling problem of maximizing the number of early jobs on a single machine. We investigate the on-line version of this problem in the Preemption-Restart model. This means that jobs may be preempted, but preempting results in all the work done on this job so far being lost. Thus, if the job is restarted, then it has to be done from scratch. We prove that the shortest remaining processing time rule yields an on-line algorithm with competitive ratio ½. Moreover, we show that there does not exist an on-line algorithm with a better performance guarantee.