Exact Algorithms for Scheduling Programs with Shared Tasks

  • Imed Kacem
  • Giorgio Lucarelli
  • Théo NazéEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1160)


We study a scheduling problem where the jobs we have to perform are composed of one or more tasks. If two jobs sharing a non-empty subset of tasks are scheduled on the same machine, then these shared tasks have to be performed only once. This kind of problem is known in the literature under the names of VM-PACKING or PAGINATION. Our objective is to schedule a set of these objects on two parallel identical machines, with the aim of minimizing the makespan. This problem is NP-complete as an extension of the PARTITION problem. In this paper we present two exact algorithms with worst-case time-complexity guarantees, by exploring different branching techniques. Our first algorithm focuses on the relation between jobs sharing one or more symbols in common, whereas the other algorithm branches on the shared symbols.


Scheduling Exact algorithms Makespan minimization 


  1. 1.
    Cygan, M., Fomin, F., Kowalik, L., Lokshtanov, D., Marx, D., Pilipczuk, M., Pilipczuk, M., Saurabh, S.: Parameterized Algorithms. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  2. 2.
    Fomin, F.V., Kratsch, D.: Exact Exponential Algorithms. Springer, Heidelberg (2010)Google Scholar
  3. 3.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Fransico (1979)zbMATHGoogle Scholar
  4. 4.
    Graham, R., Lawler, E., Lenstra, J.K., Kan, A.R.: Optimization and approximation in deterministic sequencing and scheduling: a survey (1979)Google Scholar
  5. 5.
    Grange, A., Kacem, I., Martin, S.: Algorithms for the bin packing problem with overlapping items. Comput. Ind. Eng. 115, 331–341 (2018)CrossRefGoogle Scholar
  6. 6.
    Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Martello, S., Toth, P.: Knapsack Problems: Algorithm and Computer Implementations. Wiley, Hoboken (1990)zbMATHGoogle Scholar
  8. 8.
    Sindelar, M., Sitaraman, R.K., Shenoy, P.J.: Sharing-aware algorithms for virtual machine colocation (2011)Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Laboratoire LCOMS, Université de LorraineMetzFrance

Personalised recommendations