Online Non-Preemptive Scheduling to Minimize Weighted Flow-time on Unrelated Machines

International audienceIn this paper, we consider the online problem of scheduling independent jobs non-preemptively so as to minimize the weighted flow-time on a set of unrelated machines. There has been a considerable amount of work on this problem in the preemptive setting where several competitive algorithms are known in the classical competitive model. However, the problem in the non-preemptive setting admits a strong lower bound. Recently, Lucarelli et al. presented an algorithm that achieves a O 1 2-competitive ratio when the algorithm is allowed to reject-fraction of total weight of jobs and has an-speed augmentation. They further showed that speed augmentation alone is insufficient to derive any competitive algorithm. An intriguing open question is whether there exists a scalable competitive algorithm that rejects a small fraction of total weights. In this paper, we affirmatively answer this question. Specifically, we show that there exists a O 1 3-competitive algorithm for minimizing weighted flow-time on a set of unrelated machine that rejects at most O()-fraction of total weight of jobs. The design and analysis of the algorithm is based on the primal-dual technique. Our result asserts that alternative models beyond speed augmentation should be explored when designing online schedulers in the non-preemptive setting in an effort to find provably good algorithms