Eisenbrand, Friedrich
Hähnle, Nicolai
Niemeier, Martin
Skutella, Martin
Verschae, José
Wiese, Andreas
Scheduling periodic tasks in a hard real-time environment
37th International Colloquium on Automata, Languages and Programming (ICALP2010)
37th International Colloquium on Automata, Languages and Programming (ICALP2010)
37th International Colloquium on Automata, Languages and Programming (ICALP2010)
37th International Colloquium on Automata, Languages and Programming (ICALP2010)
37
periodic scheduling
real-time scheduling
approximation algorithms
periodic maintenance problem
hardness of approximation
2010
2010
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 $\tau_i=(c_i,p_i)$ on a minimum number of identical machines and to compute offsets $a_i$ for the tasks such that no collision occurs. A task $\tau_i$ releases a job of running time $c_i$ at each time $a_i + k\cdot p_i$, $k\in\setN$ 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 $n^{1-\epsilon}$ for any $\epsilon>0$. (ii) If the periods are dividing (for each $i,j$ one has $p_i \mid p_j$ or $p_j \mid p_i$), 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 dividing case if the number of different periods is constant.
Springer-Verlag
37th International Colloquium on Automata, Languages and Programming (ICALP2010)
Conference Papers
000286345400026