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International Colloquium on Automata, Languages, and Programming

ICALP 2014: Automata, Languages, and Programming pp 625–636Cite as

How Unsplittable-Flow-Covering Helps Scheduling with Job-Dependent Cost Functions

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8572)

Abstract

Generalizing many well-known and natural scheduling problems, scheduling with job-specific cost functions has gained a lot of attention recently. In this setting, each job incurs a cost depending on its completion time, given by a private cost function, and one seeks to schedule the jobs to minimize the total sum of these costs. The framework captures many important scheduling objectives such as weighted flow time or weighted tardiness. Still, the general case as well as the mentioned special cases are far from being very well understood yet, even for only one machine. Aiming for better general understanding of this problem, in this paper we focus on the case of uniform job release dates on one machine for which the state of the art is a 4-approximation algorithm. This is true even for a special case that is equivalent to the covering version of the well-studied and prominent unsplittable flow on a path problem, which is interesting in its own right. For that covering problem, we present a quasi-polynomial time (1 + ε)-approximation algorithm that yields an (e + ε)-approximation for the above scheduling problem. Moreover, for the latter we devise the best possible resource augmentation result regarding speed: a polynomial time algorithm which computes a solution with optimal cost at 1 + ε speedup. Finally, we present an elegant QPTAS for the special case where the cost functions of the jobs fall into at most logn many classes. This algorithm allows the jobs even to have up to logn many distinct release dates. All proposed quasi-polynomial time algorithms require the input data to be quasi-polynomially bounded.

Keywords

  • Cost Function
  • Approximation Algorithm
  • Completion Time
  • Release Date
  • Polynomial Time Algorithm

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Funded by the Go8-DAAD joint research cooperation scheme.

A full version of the paper can be found at http://arxiv.org/abs/1403.1376 .

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  • DOI: 10.1007/978-3-662-43948-7_52
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Author information

Authors and Affiliations

  1. Technische Universität Berlin, Germany

    Wiebke Höhn

  2. The University of Sydney, Australia

    Julián Mestre

  3. Max-Planck-Institut für Informatik, Saarbücken, Germany

    Andreas Wiese

Authors
  1. Wiebke Höhn
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  2. Julián Mestre
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  3. Andreas Wiese
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstrasse 3, 85748, München, Germany

    Javier Esparza

  2. LIAFA, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Pierre Fraigniaud

  3. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Thore Husfeldt

  4. Department Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Elias Koutsoupias

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Höhn, W., Mestre, J., Wiese, A. (2014). How Unsplittable-Flow-Covering Helps Scheduling with Job-Dependent Cost Functions. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_52

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  • DOI: https://doi.org/10.1007/978-3-662-43948-7_52

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