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EDF-schedulability of synchronous periodic task systems is coNP-hard
Zitatschlüssel EisenbrandRothvoss2010
Autor Eisenbrand, Friedrich and Rothvoß, Thomas
Buchtitel Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA 2010)
Seiten 1029–1034
Jahr 2010
Zusammenfassung In the synchronous periodic task model, a set \tau_1,...,\tau_n of tasks is given, each releasing jobs of running time c_i with relative deadline d_i, at each integer multiple of the period p_i. It is a classical result that Earliest Deadline First (EDF) is an optimal preemptive uni-processor scheduling policy. For constrained deadlines, i.e. d_i <= p_i, the EDF-schedule is feasible if and only if for all Q >= 0: \sum_i=1^n (floor(Q-d_i)/p_i) + 1) * c_i <= Q. Though an enormous amount of literature deals with this topic, the complexity status of this test has remained unknown. We prove that testing EDF-schedulability of such a task system is (weakly) coNP-hard. This solves Problem 2 from the survey "Open Problems in Real-time Scheduling" by Baruah & Pruhs. The hardness result is achieved by applying recent results on inapproximability of Diophantine approximation.
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