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Scheduling and Fixed-Parameter Tractability

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Integer Programming and Combinatorial Optimization (IPCO 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8494))

Abstract

Fixed-parameter tractability analysis and scheduling are two core domains of combinatorial optimization which led to deep understanding of many important algorithmic questions. However, even though fixed-parameter algorithms are appealing for many reasons, no such algorithms are known for many fundamental scheduling problems.

In this paper we present the first fixed-parameter algorithms for classical scheduling problems such as makespan minimization, scheduling with job-dependent cost functions—one important example being weighted flow time—and scheduling with rejection. To this end, we identify crucial parameters that determine the problems’ complexity. In particular, we manage to cope with the problem complexity stemming from numeric input values, such as job processing times, which is usually a core bottleneck in the design of fixed-parameter algorithms. We complement our algorithms with W[1]-hardness results showing that for smaller sets of parameters the respective problems do not allow FPT-algorithms. In particular, our positive and negative results for scheduling with rejection explore a research direction proposed by Dániel Marx.

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Author information

Authors and Affiliations

  1. Cluster of Excellence MMCI, Saarbrücken, Germany

    Matthias Mnich

  2. Max Planck Institute for Computer Science, Saarbrücken, Germany

    Andreas Wiese

Authors
  1. Matthias Mnich
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  2. Andreas Wiese
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Editor information

Editors and Affiliations

  1. Department of Industrial and Operations Engineering, University of Michigan, Beal Avenue, 1205, Ann Arbor, MI, USA

    Jon Lee

  2. Research Institute for Discrete Mathematics, University of Bonn, Lennéstr. 2, P.O. Box, 53113, Bonn, Germany

    Jens Vygen

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Mnich, M., Wiese, A. (2014). Scheduling and Fixed-Parameter Tractability. In: Lee, J., Vygen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2014. Lecture Notes in Computer Science, vol 8494. Springer, Cham. https://doi.org/10.1007/978-3-319-07557-0_32

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  • DOI: https://doi.org/10.1007/978-3-319-07557-0_32

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07556-3

  • Online ISBN: 978-3-319-07557-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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