eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2010-05-03
1
3
10.4230/DagSemProc.10071.13
article
Scheduling periodic tasks in a hard real-time environment
Eisenbrand, Friedrich
Hähnle, Nicolai
Niemeier, Martin
Skutella, Martin
Verschae, Jose
Wiese, Andreas
We consider a real-time scheduling problem that occurs in the design
of software-based aircraft control. The goal is to distribute tasks
$ au_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 $ au_i$ releases a job of running time $c_i$ at each time $a_i +
kcdot p_i, , k in mathbb{N}_0$ and a collision occurs if two jobs are
simultaneously active on the same machine.
We shed some light on the complexity and approximability landscape of this problem.
Although the problem cannot be approximated
within a factor of $n^{1-varepsilon}$ for any $varepsilon>0$, an interesting restriction
is much more tractable: If the periods are dividing (for each $i,j$ one has $p_i |
p_j$ or $p_j | p_i$), the problem allows for a better structured representation of solutions, which leads
to a 2-approximation. This result is tight, even asymptotically.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol10071/DagSemProc.10071.13/DagSemProc.10071.13.pdf
Real-Time Scheduling
Periodic scheduling problem
Periodic maintenance problem
Approximation hardness
Approximation algorithm