Dedicated Scheduling of Biprocessor Tasks to Minimize Mean Flow Time

  • Krzysztof Giaro
  • Marek Kubale
  • Michał Małafiejski
  • Konrad Piwakowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2328)


This paper investigates the complexity of scheduling biprocessor tasks on dedicated processors to minimize mean flow time. Since the general problem is strongly NP-hard, we assume some restrictions on task lengths and the structure of associated scheduling graphs. Of particular interest are acyclic graphs. In this way we identify a borderline between NP-hard and polynomially solvable special cases.


Bipartite Graph Optimal Schedule Total Completion Time Initial Task Double Star 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Coffman, Jr., E.G., Garey, M.R., Johnson, D.S., LaPaugh, A.S.: Scheduling file transfers. SIAM J. Comput. 14 (1985) 744–780MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Cole, R., Ost, K., Schirra, S., Edge-coloring bipartite graphs in O(E logD) time. Combinatorica 21 (2001) 5–12MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Dobson, G., Karmarkar, U.S.: Simultaneous resourse scheduling to minimize weighted flow times. Oper. Res. 37 (1989) 592–600MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Drozdowski, M.: Scheduling multiprocessor tasks-An overview. Euro. J. Oper. Res. 94 (1996) 215–230zbMATHCrossRefGoogle Scholar
  5. 5.
    Drozdowski, M., Dell’Olmo, P.: Scheduling multiprocessor tasks for mean flow time criterion. Comp. Oper. Res. 27 (2000) 571–585MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Gehringer, E.F., Siewiorek, D.P., Segall, Z.: Parallel Processing: The Cm* Experience. Digital Press, Bedford (1987)Google Scholar
  7. 7.
    Giaro, K., Kubale, M., MaFlafiejski, M., Piwakowski, K.: Chromatic scheduling of dedicated 2-processor UET tasks to minimize mean flow time. Proc. ETFA’99, Barcelona (1999) 343–347Google Scholar
  8. 8.
    Giaro, K., Kubale, M.: Edge-chromatic sum of trees and bounded cyclicity graphs. Inf. Process. Lett. 75 (2000) 65–69MathSciNetCrossRefGoogle Scholar
  9. 9.
    Giaro, K., Kubale, M., Piwakowski, K.: Complexity results on open shop scheduling to minimize weighted mean flow time of operations. (in preparation)Google Scholar
  10. 10.
    Halldórsson, M.M., Kortsarz, G., Proskurowski, A., Salman, R., Shachnai, H., Telle, J.A., Multicoloring trees. Computing and Combinatorics Conference, Tokyo (1999), Lecture Notes in Computer Science 1627 (1999) 271–280CrossRefGoogle Scholar
  11. 11.
    Hoogeveen, J.A., van de Velde, S.L., Veltman, B.: Complexity of scheduling multiprocessor tasks with prespecified processor allocations. Disc. Appl. Math. 55 (1994) 259–272zbMATHCrossRefGoogle Scholar
  12. 12.
    Krawczyk, H., Kubale, M.: An approximation algorithm for diagnostic test scheduling in multicomputer systems. IEEE Trans. Comput. 34 (1985) 869–872CrossRefGoogle Scholar
  13. 13.
    Kubale, M.: The complexity of scheduling independent two-processor tasks on dedicated processors. Inf. Process. Lett. 24 (1987) 141–147MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Kubale, M.: Preemptive versus nonpreemptive scheduling of biprocessor tasks on dedicated processors. Euro. J. Oper. Res. 94 (1996) 242–251zbMATHCrossRefGoogle Scholar
  15. 15.
    Kubale, M., Piwakowski, K.: A linear algorithm for edge coloring of binomial trees. Disc. Math. 150 (1996) 247–256MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Zhou, X., Nishizeki, T.: Algorithms for the cost edge-coloring of tress. Lecture Notes in Computer Science 2108 (2001) 288–297Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Krzysztof Giaro
    • 1
  • Marek Kubale
    • 1
  • Michał Małafiejski
    • 1
  • Konrad Piwakowski
    • 1
  1. 1.Foundations of Informatics Dept.Technical University of GdańskGdańskPoland

Personalised recommendations