The Complexity of Scheduling for p-Norms of Flow and Stretch - (Extended Abstract)

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,∞).