Approximation schemes for preemptive weighted flow time
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We consider computing optimal k-norm preemptive schedules of jobs that arrive over time. In particular, we show that computing the optimal k-norm of flow schedule, 1 |rj, pmtn |∑j (Cj−rj)k in standard 3-field scheduling notation, is strongly NP-hard for k∈(0, 1) and integers k∈(1,∞). Further we show that computing the optimal k-norm of stretch schedule, 1 |rj, pmtn |∑j ((Cj−rj)/pj)k in standard 3-field scheduling notation, is strongly NP-hard for k∈(0, 1) and integers k∈∪(1,∞).