Periodic multiprocessor scheduling
PARLE '91 Proceedings on Parallel architectures and languages Europe : volume I: parallel architectures and algorithms: volume I: parallel architectures and algorithms
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MFCS '90 Selected papers of the 15th international symposium on Mathematical foundations of computer science
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Mathematics of Operations Research
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SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
The mixing-MIR set with divisible capacities
Mathematical Programming: Series A and B
The mixing set with divisible capacities
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Solving an avionics real-time scheduling problem by advanced IP-methods
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Strictly periodic scheduling in IMA-based architectures
Real-Time Systems
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We give a rigorous account on the complexity landscape of an important real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks τi = (ci, pi) on a minimum number of identical machines and to compute offsets ai for the tasks such that no collision occurs. A task τi releases a job of running time ci; at each time ai + k ċ pi, k ∈ N0 and a collision occurs if two jobs are simultaneously active on the same machine. Our main results are as follows: (i) We show that the minimization problem cannot be approximated within a factor of n1-ε for any ε 0. (ii) If the periods are harmonic (for each i, j one has pi | pj or pj | pi), then there exists a 2-approximation for the minimization problem and this result is tight, even asymptotically. (iii) We provide asymptotic approximation schemes in the harmonic case if the number of different periods is constant.