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

René Bevern (), Rolf Niedermeier () and Ondřej Suchý ()
Additional contact information
René Bevern: Novosibirsk State University
Rolf Niedermeier: TU Berlin
Ondřej Suchý: Czech Technical University in Prague

Journal of Scheduling, 2017, vol. 20, issue 3, No 3, 255-265

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

Keywords: Release times and deadlines; Machine minimization; Sequencing within intervals; Shiftable intervals; Fixed-parameter tractability; NP-hard problem (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10951-016-0478-9

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