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Busy Time Scheduling on a Bounded Number of Machines (Extended Abstract)

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Algorithms and Data Structures (WADS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10389))

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Abstract

In this paper we consider a basic scheduling problem called the busy time scheduling problem - given n jobs, with release times \(r_j\), deadlines \(d_j\) and processing times \(p_j\), and m machines, where each machine can run up to g jobs concurrently, our goal is to find a schedule to minimize the sum of the “on” times for the machines. We develop the first correct constant factor online competitive algorithm for the case when g is unbounded, and give a \(O(\log P)\) approximation for general g, where P is the ratio of maximum to minimum processing time. When g is bounded, all prior busy time approximation algorithms use an unbounded number of machines; note it is NP-hard just to test feasibility on fixed m machines. For this problem we give both offline and online (requiring “lookahead”) algorithms, which are O(1) competitive in busy time and \(O(\log P)\) competitive in number of machines used.

Full version: http://math.mit.edu/~fkoehler/busytime.pdf. Research supported by CCF 1217890 and CNS 1262805.

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Author information

Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    Frederic Koehler

  2. Department of Computer Science, University of Maryland, College Park, MD, 20742, USA

    Samir Khuller

Authors
  1. Frederic Koehler
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  2. Samir Khuller
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Corresponding author

Correspondence to Frederic Koehler .

Editor information

Editors and Affiliations

  1. Computer Science, University of Toronto , Toronto, Ontario, Canada

    Faith Ellen

  2. Computer Science, Memorial University of Newfoundland , St. John’s, Newfoundland and Labrador, Canada

    Antonina Kolokolova

  3. Carleton University, Ottawa, Ontario, Canada

    Jörg-Rüdiger Sack

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Koehler, F., Khuller, S. (2017). Busy Time Scheduling on a Bounded Number of Machines (Extended Abstract). In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_44

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  • DOI: https://doi.org/10.1007/978-3-319-62127-2_44

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62126-5

  • Online ISBN: 978-3-319-62127-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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