EDF-schedulability of synchronous periodic task systems is coNP-hard

Research Area: Algorithm Engineering for Real-time Scheduling and Routing Year: 2010
Type of Publication: In Proceedings Keywords: periodic scheduling; complexity theory
Authors: Friedrich Eisenbrand; Thomas Rothvoß
Book title: 21st {S}ymposium on {D}iscrete {A}lgorithms ({SODA} 2010)
Pages: 1029-1034
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 = 0: \sum_{i=1}^n (floor(Q-d_i)/p_i) + 1) * c_i ls 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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