Online preemptive scheduling with immediate decision or notification and penalties

Abstract

We consider online preemptive scheduling problems where jobs have deadlines and the objective is to maximize the total value of jobs completed before their deadlines. In the first problem, preemptions are not free but incur a penalty. In the second problem, a job has to be accepted or rejected immediately upon arrival, and possibly allocated a fixed scheduling interval as well; if these accepted jobs are eventually not completed they incur a penalty (on top of not getting the value of the job). We give an algorithm with the optimal competitive ratio for the first problem, and new and improved algorithms for the second problem. © 2010 Springer-Verlag Berlin Heidelberg.