Improved online algorithms for the batch scheduling of equal-length jobs with incompatible families to maximize the weighted number of early jobs

摘要

We consider the online scheduling of equal-length jobs with incompatible families on m identical batch machines. Each job has a release time, a deadline and a weight. Each batch machine can process up to b jobs (which come from the same family) simultaneously as a batch, where b is called the capacity of the machines. Our goal is to determine a preemption-restart schedule which maximizes the weighted number of early jobs. For this problem, Li et al. (Inf Process Lett 112:503–508, 2012) provided an online algorithm of competitive ratio 3+22~(1/2) for both b =∞and b < ∞. In this paper, we study two special cases of this problem. For the case that m = 2, we first present a lower bound 2, and then provide an online algorithm with a competitive ratio of 3 for both b = ∞and b < ∞. For the case in which m = 3, b = ∞and all jobs come from a common family, we present an online algorithm with a competitive ratio of (8 + 2 15~(1/2))/3 ≈ 5.249.