The complexity of scheduling trees with communication delays

Extended abstract
  • Jan Karel Lenstra
  • Marinus Veldhorst
  • Bart Veltman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 726)


We consider the problem of finding a minimum-length schedule on m machines for a set of n unit-length tasks with a forest of intrees as precedence relation, and with unit interprocessor communication delays. First we prove that this problem is NP-complete; second we derive a linear time algorithm for the special case that m equals 2.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. Afrati, C. H. Papadimitriou, and G. Papageorgiou. Scheduling dags to minimize time and communication. In Proc. 3rd Conf. VLSI Algorithms and Architectures AWOC, LNCS, vol. 319, pages 134–138, Springer-Verlag, Berlin, 1988.Google Scholar
  2. 2.
    F. D. Anger, J.-J. Hwang, and Y.-C. Chow. Scheduling with sufficient loosely coupled processors. J. of Parallel and Distributed Computing, 9:87–92, 1990.Google Scholar
  3. 3.
    P. Chrétienne. A polynomial algorithm to optimally schedule tasks on a virtual distributed system under tree-like precedence constraints. Europ. Jrnl. Operational Res., 43:225–230, 1989.Google Scholar
  4. 4.
    P. Chrétienne and C. Picouleau. The basic scheduling problem with interprocessor communication delays. In Proc. Summerschool on Scheduling Theory and its Applications, Bonas, France, pages 81–100. INRIA, 1992.Google Scholar
  5. 5.
    M. Fujii, T. Kasami, and K. Ninomiya. Optimal sequencing of two equivalent processors. SIAM J. Appl. Math., 17:784–789, 1969. Erratum. SIAM J. Appl. Math. 20:141, 1971.Google Scholar
  6. 6.
    M. R. Garey and D. S. Johnson. Computers and Intractability, A guide to the theory of NP-completeness. W. H. Freeman and Co., San Francisco, CA, 1979.Google Scholar
  7. 7.
    J. A. Hoogeveen, B. Veltman, and J. K. Lenstra. Three, four, five, six, or the complexity of scheduling with communication delays. Technical Report BS-R9229, CWI, Amsterdam, The Netherlands, 1992.Google Scholar
  8. 8.
    T. C. Hu. Parallel sequencing and assembly line problems. Operations Res., 9:841–848, 1961.Google Scholar
  9. 9.
    C. Picouleau. Etude de problèmes d'optimisation dans les systèmes distribués. PhD thesis, Univers. Pierre et Marie Curie, Paris, France, 1992.Google Scholar
  10. 10.
    M. L. Prastein. Precedence-constrained scheduling with minimum time and communication. Technical Report UILU-ENG-87-2207, ACT-75, Coordinated Science Laboratory, Dpt of CS, Univ of Illinois at Urbana-Champaign, Urbana-Champaign, IL, USA, 1987.Google Scholar
  11. 11.
    J. D. Ullmann. NP-complete scheduling problems. J. Comput. Syst. Sci., 10:384–393, 1975.Google Scholar
  12. 12.
    T. A. Varvarigou, V. P. Roychowdhury, and T. Kailath. Scheduling in and out forests in the presence of communication delays, 1992. Unpublished manuscript.Google Scholar
  13. 13.
    B. Veltman. Multiprocessor scheduling with communication delays. PhD thesis, Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands, 1993.Google Scholar
  14. 14.
    B. Veltman, B. J. Lageweg, and J. K. Lenstra. Multiprocessor scheduling with communication delays. Parallel Computing, 16:173–182, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Jan Karel Lenstra
    • 1
  • Marinus Veldhorst
    • 2
  • Bart Veltman
    • 1
  1. 1.Department of Mathematics and Computing ScienceEindhoven University of TechnologyMB EindhovenThe Netherlands
  2. 2.Department of Computer ScienceUtrecht UniversityTB UtrechtThe Netherlands

Personalised recommendations