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We consider the NP-hard preemptive single-machine scheduling problem to minimize the total weighted completion time subject to release dates. A natural extension of Smith's ratio rule is to preempt the currently active job whenever a new job arrives that has higher ratio of weight to processing time. We prove that the competitive ratio of this simple on-line algorithm is precisely 2. We also show that list scheduling in order of random α-points drawn from the same schedule results in an on-line algorithm with competitive ratio . Since its analysis relies on a well-known integer programming relaxation of the scheduling problem, the relaxation has performance guarantee as well. On the other hand, we show that it is at best an -relaxation. Copyright © 2002 John Wiley & Sons, Ltd.
Schulz et al. (Tue,) studied this question.