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Scheduling and Fixed-Parameter Tractability

  • Matthias Mnich
  • Andreas Wiese
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Processing Time Schedule Problem Completion Time Polynomial Time Approximation Scheme Unrelated Parallel Machine 
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.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Matthias Mnich
    • 1
  • Andreas Wiese
    • 2
  1. 1.Cluster of Excellence MMCISaarbrückenGermany
  2. 2.Max Planck Institute for Computer ScienceSaarbrückenGermany

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