Open-Shop Scheduling for Unit Jobs Under Precedence Constraints
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.
KeywordsOpen-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.
- 4.Brucker, P., Knust, S.: Complexity results for scheduling problems (2009). http://www2.informatik.uni-osnabrueck.de/knust/class/
- 5.Dürr, C.: The scheduling zoo (2016). http://schedulingzoo.lip6.fr