Journal of Scheduling

, Volume 20, Issue 3, pp 255–265 | Cite as

A parameterized complexity view on non-preemptively scheduling interval-constrained jobs: few machines, small looseness, and small slack

  • René van Bevern
  • Rolf Niedermeier
  • Ondřej Suchý
Article

Abstract

We study the problem of non-preemptively scheduling n jobs, each job j with a release time \(t_j\), a deadline \(d_j\), and a processing time \(p_j\), on m parallel identical machines. Cieliebak et al. (2004) considered the two constraints \(|d_j-t_j|\le \lambda {}p_j\) and \(|d_j-t_j|\le p_j +\sigma \) and showed the problem to be NP-hard for any \(\lambda >1\) and for any \(\sigma \ge 2\). We complement their results by parameterized complexity studies: we show that, for any \(\lambda >1\), the problem remains weakly NP-hard even for \(m=2\) and strongly W[1]-hard parameterized by m. We present a pseudo-polynomial-time algorithm for constant m and \(\lambda \) and a fixed-parameter tractability result for the parameter m combined with \(\sigma \).

Keywords

Release times and deadlines Machine minimization Sequencing within intervals Shiftable intervals Fixed-parameter tractability NP-hard problem 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • René van Bevern
    • 1
  • Rolf Niedermeier
    • 2
  • Ondřej Suchý
    • 3
  1. 1.Novosibirsk State UniversityNovosibirskRussian Federation
  2. 2.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany
  3. 3.Faculty of Information TechnologyCzech Technical University in PraguePragueCzech Republic

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