Open-Shop Scheduling for Unit Jobs Under Precedence Constraints

  • An Zhang
  • Yong Chen
  • Randy Goebel
  • Guohui LinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11346)


We study open-shop scheduling for unit jobs under precedence constraints, where if one job precedes another job then it has to be finished before the other job can start to be processed. For the three-machine open-shop to minimize the makespan, we first present a simple 5/3-approximation based on a partition of the job set into agreeable layers using the natural layered representation of the precedence graph. We then show a greedy algorithm to reduce the number of singleton-job layers, resulting in an improved partition, which leads to a 4/3-approximation. Both approximation algorithms apply to the general m-machine open-shops too.


Open-shop scheduling Precedence constraint Directed acyclic graph Approximation algorithm 



This research is partially supported by the NSFC Grants 11571252, 11771114 and 61672323, the China Scholarship Council Grant 201508330054, and the NSERC Canada.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • An Zhang
    • 1
    • 2
  • Yong Chen
    • 1
    • 2
  • Randy Goebel
    • 2
  • Guohui Lin
    • 2
    Email author
  1. 1.Department of MathematicsHangzhou Dianzi UniversityHangzhouChina
  2. 2.Department of Computing ScienceUniversity of AlbertaEdmontonCanada

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