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URN: urn:nbn:de:0030-drops-25458
URL: http://drops.dagstuhl.de/opus/volltexte/2010/2545/
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Eisenbrand, Friedrich ; Rothvoss, Thomas

Recent Hardness Results for Periodic Uni-processor Scheduling

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Abstract

Consider a set of $n$ periodic tasks $ au_1,ldots, au_n$ where $ au_i$ is described by an execution time $c_i$, a (relative) deadline $d_i$ and a period $p_i$. We assume that jobs are released synchronously (i.e. at each multiple of $p_i$) and consider pre-emptive, uni-processor schedules. We show that computing the response time of a task $ au_n$ in a Rate-monotonic schedule i.e. computing [ minleft{ r geq mid c_n + sum_{i=1}^{n-1} leftlceil frac{r}{p_i} ight ceil c_i leq r ight} ] is (weakly) $mathbf{NP}$-hard (where $ au_n$ has the lowest priority and the deadlines are implicit, i.e. $d_i = p_i$). Furthermore we obtain that verifying EDF-schedulability, i.e. [ forall Q geq 0: sum_{i=1}^n left( leftlfloor frac{Q-d_i}{p_i} ight floor +1 ight)cdot c_i leq Q ] for constrained-deadline tasks ($d_i leq p_i$) is weakly $mathbf{coNP}$-hard.

BibTeX - Entry

@InProceedings{eisenbrand_et_al:DSP:2010:2545,
  author =	{Friedrich Eisenbrand and Thomas Rothvoss},
  title =	{Recent Hardness Results for Periodic Uni-processor Scheduling},
  booktitle =	{Scheduling},
  year =	{2010},
  editor =	{Susanne Albers and Sanjoy K. Baruah and Rolf H. M{\"o}hring and Kirk Pruhs},
  number =	{10071},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2545},
  annote =	{Keywords: Hardness, periodic scheduling, uni-processor scheduling}
}

Keywords: Hardness, periodic scheduling, uni-processor scheduling
Seminar: 10071 - Scheduling
Issue Date: 2010
Date of publication: 03.05.2010


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