On the NP-hardness of scheduling with time restrictions

An Zhang, Yong Chen, Lin Chen, Guangting Chen

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

In a recent paper, Braun et al. (2014) have addressed a single-processor scheduling problem with time restrictions. Given a fixed integer B≥2, there is a set of jobs to be processed by a single processor subject to the following B-constraint. For any real x, no unit time interval [x,x+1) is allowed to intersect more than B jobs. The makespan minimization problem has been shown to be NP-hard when B is a part of input and left as an open question whether it remains NP-hard or not if B is fixed (Braun et al., 2014; 2016; Zhang, 2017). This paper contributes to answering this question that we prove the problem is NP-hard even when B=2. A PTAS is also presented for any constant B≥2.

Original languageEnglish
Pages (from-to)54-62
Number of pages9
JournalDiscrete Optimization
Volume28
DOIs
StatePublished - May 2018

Keywords

  • NP-hardness
  • Single-processor scheduling
  • Time restrictions

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