Abstract
We study the nonpreemptive online scheduling of jobs with deadlines and weights. The goal of the scheduling algorithm is to maximize the total weight of jobs completed by their deadlines. As a special case, the weights may be given as the processing times of jobs, where the job instance is said to have uniform value density. Most previous work of nonpreemptively scheduling jobs online concentrates on a single machine and uniform value density. For the single machine, Goldwasser [6] shows a matching upper bound and lower bound of $(2 + \frac{1}{\kappa})$ on the best competitive ratio, where every job can be delayed for at least κ times its processing time before meeting its deadline. This paper is concerned with multiple machines. We provide a $(7 + 3\sqrt{\frac{1}{\kappa}})$-competitive algorithm defined on multiple machines. Also we consider arbitrary value density, where jobs have arbitrary weights. We derive online scheduling algorithms on a single machine as well as on multiple machines.
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