Bounds for Scheduling Jobs on Grid Processors

  • Joan Boyar
  • Faith Ellen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8066)


In the Grid Scheduling problem, there is a set of jobs each with a positive integral memory requirement. Processors arrive in an online manner and each is assigned a maximal subset of the remaining jobs such that the sum of the memory requirements of those jobs does not exceed the processor’s memory capacity. The goal is to assign all the jobs to processors so as to minimize the sum of the memory capacities of the processors that are assigned at least one job. Previously, a lower bound of \(\frac{5}{4}\) on the competitive ratio of this problem was achieved using jobs of size S and 2S − 1. For this case, we obtain matching upper and lower bounds, which vary depending on the ratio of the number of small jobs to the number of large jobs.


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  1. 1.
    Boyar, J., Favrholdt, L.M.: Scheduling jobs on Grid processors. Algorithmica 57(4), 819–847 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Boyar, J., Favrholdt, L.M.: A new variable-sized bin packing problem. Journal of Scheduling 15, 273–287 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Epstein, L., Levin, A.: More online bin packing with two item sizes. Discrete Optimization 5(4), 705–713 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Gutin, G., Jensen, T.R., Yeo, A.: On-line bin packing with two item sizes. Algorithmic Operations Research 1(2) (2006)Google Scholar
  5. 5.
    Karlin, A.R., Manasse, M.S., Rudolph, L., Sleator, D.D.: Competitive snoopy caching. Algorithmica 3(1), 79–119 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Liang, F.M.: A lower bound for on-line bin packing. Inform. Process. Lett. 10, 76–79 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Comm. of the ACM 28(2), 202–208 (1985)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Zhang, G.: A new version of on-line variable-sized bin packing. Discrete Applied Mathematics 72, 193–197 (1997)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Joan Boyar
    • 1
  • Faith Ellen
    • 2
  1. 1.University of Southern DenmarkDenmark
  2. 2.University of TorontoCanada

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