### 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 language | English |
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Pages (from-to) | 54-62 |

Number of pages | 9 |

Journal | Discrete Optimization |

Volume | 28 |

DOIs | |

State | Published - May 2018 |

### Keywords

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

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## Cite this

*Discrete Optimization*,

*28*, 54-62. https://doi.org/10.1016/j.disopt.2017.12.001