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Parameterized Complexity of a Parallel Machine Scheduling Problem

Authors Maher Mallem , Claire Hanen , Alix Munier-Kordon

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Maher Mallem
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
Claire Hanen
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
  • Université Paris Nanterre, UPL, 92000 Nanterre, France
Alix Munier-Kordon
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France

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Maher Mallem, Claire Hanen, and Alix Munier-Kordon. Parameterized Complexity of a Parallel Machine Scheduling Problem. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 21:1-21:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.IPEC.2022.21

Abstract

In this paper we consider the parameterized complexity of two versions of a parallel machine scheduling problem with precedence delays, unit processing times and time windows. In the first version - with exact delays - we assume that the delay between two jobs must be exactly respected, whereas in the second version - with minimum delays - the delay between two jobs is a lower bound on the time between them. Two parameters are considered for this analysis: the pathwidth of the interval graph induced by the time windows and the maximum precedence delay value. We prove that our problems are para-NP-complete with respect to any of the two parameters and fixed-parameter tractable parameterized by the pair of parameters.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • parameterized complexity
  • scheduling
  • precedence delays
  • pathwidth
  • chains
  • parallel processors

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