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Competitive Analysis of Scheduling Algorithms for Aggregated Links

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Abstract

We study an online job scheduling problem arising in networks with aggregated links. The goal is to schedule n jobs, divided into k disjoint chains, on m identical machines, without preemption, so that the jobs within each chain complete in the order of release times and the maximum flow time is minimized.

We present a deterministic online algorithm \(\mathsf{Block}\) with competitive ratio \(O(\sqrt{n/m})\) , and show a matching lower bound, even for randomized algorithms. The performance bound for \(\mathsf{Block}\) we derive in the paper is, in fact, more subtle than a standard competitive ratio bound, and it shows that in overload conditions (when many jobs are released in a short amount of time), \(\mathsf{Block}\) ’s performance is close to the optimum.

We also show how to compute an offline solution efficiently for k=1, and that minimizing the maximum flow time for k,m≥2 is \({ \mathcal {N}\mathcal {P}}\) -hard. As by-products of our method, we obtain two offline polynomial-time algorithms for minimizing makespan: an optimal algorithm for k=1, and a 2-approximation algorithm for any k.

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Authors and Affiliations

  1. Department of Computer Science, University of California, Riverside, CA, 92521, USA

    Wojciech Jawor & Marek Chrobak

  2. CNRS, Laboratoire d’Informatique de l’Ecole Polytechnique, 91128, Palaiseau, France

    Christoph Dürr

Authors
  1. Wojciech Jawor
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  2. Marek Chrobak
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  3. Christoph Dürr
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Corresponding author

Correspondence to Marek Chrobak.

Additional information

W. Jawor and M. Chrobak supported by NSF grants OISE-0340752 and CCR-0208856.

Work of C. Dürr conducted while being affiliated with the Laboratoire de Recherche en Informatique, Université Paris-Sud, 91405 Orsay. Supported by the CNRS/NSF grant 17171 and ANR Alpage.

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Jawor, W., Chrobak, M. & Dürr, C. Competitive Analysis of Scheduling Algorithms for Aggregated Links. Algorithmica 51, 367–386 (2008). https://doi.org/10.1007/s00453-007-9053-2

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  • DOI: https://doi.org/10.1007/s00453-007-9053-2

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