Advertisement

Chromatic Scheduling of 1- and 2-Processor UET Tasks on Dedicated Machines with Availability Constraints

  • Krzysztof Giaro
  • Marek Kubale
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3911)

Abstract

We address a generalization of the classical 1- and 2-processor UET scheduling problem on dedicated machines. In our chromatic model of scheduling machines have non-simultaneous availability times and tasks have arbitrary release times and due dates. Also, the versatility of our approach makes it possible to generalize all known classical criteria of optimality. Under these constraints we show that the problem of optimal scheduling of sparse instances can be solved in polynomial time.

Keywords

Availability Constraint Test Schedul Pendant Edge Optimal Coloring Multiprocessor Task 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bianco, L., Błażewicz, J., Dell’Olmo, P., Drozdowski, M.: Preemptive multiprocessor task scheduling with release times and time windows. Ann. Oper. Res. 70, 43–55 (1997)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Błażewicz, J., Dell’Olmo, P., Drozdowski, M., Ma̧czka, P.: Scheduling multiprocessor tasks on parallel processors with limited availability. Euro. J. Oper. Res. 149, 377–389 (2003)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Błażewicz, J., Dell’Olmo, P., Drozdowski, M., Speranza, M.G.: Scheduling multiprocessor tasks on three dedicated processors. Infor. Process. Lett. 41, 275–280 (1992), Corrigendum IPL 49, 269–270 (1994)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Coffman Jr., E.G., Garey, M.R., Johnson, D.S., LaPaugh, A.S.: Scheduling file transfers. SIAM J. Comput. 14, 744–780 (1985)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Dobson, G.S., Karmarkar, U.S.: Simultaneous resource scheduling to minimize weighted flow times. Oper. Res. 37, 592–600 (1989)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Drozdowski, M.: Scheduling multiprocessor tasks - An overview. J. Oper. Res. 94, 215–230 (1996)CrossRefMATHGoogle Scholar
  7. 7.
    Gehringer, E.F., Siewiorek, D.P., Segall, Z.: Parallel Processing: The Cm* Experience. Digital Press, Bedford (1987)Google Scholar
  8. 8.
    Gharbi, A., Haouari, M.: Optimal parallel machines scheduling with availability constraints. Disc. Appl. Math. 148, 63–87 (2005)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Giaro, K., Kubale, M.: Edge-chromatic sum of trees and bounded cyclicity graphs. Infor. Process. Lett. 75, 65–69 (2000)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Giaro, K., Kubale, M., Piwakowski, K.: Complexity results on open schop scheduling to minimize total cost of operations. Intern. J. Comp. Sys. Sign. 3, 84–91 (2002)Google Scholar
  11. 11.
    Kao, M., Lam, T., Sung, W., Ting, H.: All-cavity maximum matchings. Proc. Inf. Syst. E-87, 364–373 (2004)MATHGoogle Scholar
  12. 12.
    Krawczyk, H., Kubale, M.: An approximation algorithm for diagnostic test scheduling in multicomputer systems. IEEE Trans. Comp. 34, 869–872 (1985)CrossRefGoogle Scholar
  13. 13.
    Kubale, M.: The complexity of scheduling independent two-processor tasks on dedicated processors. Infor. Process. Lett. 24, 141–147 (1987)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Kubale, M.: Preemptive versus nonpreemptive scheduling of biprocessor tasks on dedicated prosessors. Euro. J. Oper. Res. 94, 242–251 (1996)CrossRefMATHGoogle Scholar
  15. 15.
    Lloyd, E.L.: Concurrent task systems. Oper. Res. 29, 189–201 (1981)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Zhou, X., Nishizeki, T.: Algorithms for the cost edge-coloring of trees. In: Wang, J. (ed.) COCOON 2001. LNCS, vol. 2108, pp. 288–297. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Krzysztof Giaro
    • 1
  • Marek Kubale
    • 1
  1. 1.Department of Algorithms and System ModelingGdańsk University of TechnologyPoland

Personalised recommendations