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Online scheduling of jobs with kind release times and deadlines on a single machine

  • Wen-jie Li
  • Ran Ma
  • Qi Feng
Article
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Abstract

This paper studies online scheduling of jobs with kind release times on a single machine. Here “kind release time” means that in online setting, no jobs can be released when the machine is busy. Each job J has a kind release time r(J) ≥ 0, a processing time p(J) > 0 and a deadline d(J) > 0. The goal is to determine a schedule which maximizes total processing time (Σp(J)E(J)) or total number (ΣE(J)) of the accepted jobs. For the first objective function Σp(J)E(J), we first present a lower bound \(\sqrt 2 \), and then provide an online algorithm LEJ with a competitive ratio of 3. This is the first deterministic algorithm for the problem with a constant competitive ratio. When p(J) ∈ {1, k}, k > 1 is a real number, we first present a lower bound min{(1+k)/k, 2k/(1+k)}, and then we show that LEJ has a competitive ratio of 1+⌈k⌉/k. In particular, when all the k length jobs have tight deadlines, we first present a lower bound max{4/(2 + k), 1} (for Σp(J)E(J)) and 4/3 (for ΣE(J)). Then we prove that LEJ is ⌈k⌉/k-competitive for Σp(J)E(J) and we provide an online algorithm H with a competitive ratio of 2⌈k⌉/(⌈k⌉ + 1) for the second objective function ΣE(J).

Keywords

scheduling online algorithm kind release time deadline 

MR Subject Classification

90B36 90C39 

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Copyright information

© Editorial Committee of Applied Mathematics 2019

Authors and Affiliations

  • Wen-jie Li
    • 1
  • Ran Ma
    • 2
  • Qi Feng
    • 3
  1. 1.School of Mathematical SciencesLuoyang Normal UniversityLuoyang, HenanPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsQingdao UniversityQingdao, ShandongPeople’s Republic of China
  3. 3.Department of Information and Computation ScienceZhongyuan University of TechnologyZhengzhou, HenanPeople’s Republic of China

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