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Scheduling with Testing on Multiple Identical Parallel Machines

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Algorithms and Data Structures (WADS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12808))

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Abstract

Scheduling with testing is a recent online problem within the framework of explorable uncertainty motivated by environments where some preliminary action can influence the duration of a task. Jobs have an unknown processing time that can be explored by running a test. Alternatively, jobs can be executed for the duration of a given upper limit. We consider this problem within the setting of multiple identical parallel machines and present competitive deterministic algorithms and lower bounds for the objective of minimizing the makespan of the schedule. In the non-preemptive setting, we present the SBS algorithm whose competitive ratio approaches 3.1016 if the number of machines becomes large. We compare this result with a simple greedy strategy and a lower bound which approaches 2. In the case of uniform testing times, we can improve the SBS algorithm to be 3-competitive. For the preemptive case we provide a 2-competitive algorithm and a tight lower bound which approaches the same value.

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 277991500/GRK2201, and by the European Research Council, Grant Agreement No. 691672.

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Author information

Authors and Affiliations

  1. Department of Informatics, Technical University of Munich, Boltzmannstr. 3, 85748, Garching, Germany

    Susanne Albers & Alexander Eckl

  2. Advanced Optimization in a Networked Economy, Technical University of Munich, Arcisstraße 21, 80333, Munich, Germany

    Alexander Eckl

Authors
  1. Susanne Albers
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  2. Alexander Eckl
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Correspondence to Alexander Eckl .

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Editors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada

    Anna Lubiw

  2. University of Alberta, Edmonton, AB, Canada

    Mohammad Salavatipour

  3. Dalhousie University, Halifax, Canada

    Meng He

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Albers, S., Eckl, A. (2021). Scheduling with Testing on Multiple Identical Parallel Machines. In: Lubiw, A., Salavatipour, M., He, M. (eds) Algorithms and Data Structures. WADS 2021. Lecture Notes in Computer Science(), vol 12808. Springer, Cham. https://doi.org/10.1007/978-3-030-83508-8_3

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  • DOI: https://doi.org/10.1007/978-3-030-83508-8_3

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  • Online ISBN: 978-3-030-83508-8

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