Abstract
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.
This research was supported in part by the Danish Council for Independent Research, Natural Sciences (FNU), the VELUX Foundation, and the Natural Science and Engineering Research Council of Canada (NSERC). Parts of this work were carried out while Joan Boyar was visiting University of Waterloo and University of Toronto and while Faith Ellen was visiting University of Southern Denmark.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Boyar, J., Favrholdt, L.M.: Scheduling jobs on Grid processors. Algorithmica 57(4), 819–847 (2010)
Boyar, J., Favrholdt, L.M.: A new variable-sized bin packing problem. Journal of Scheduling 15, 273–287 (2012)
Epstein, L., Levin, A.: More online bin packing with two item sizes. Discrete Optimization 5(4), 705–713 (2008)
Gutin, G., Jensen, T.R., Yeo, A.: On-line bin packing with two item sizes. Algorithmic Operations Research 1(2) (2006)
Karlin, A.R., Manasse, M.S., Rudolph, L., Sleator, D.D.: Competitive snoopy caching. Algorithmica 3(1), 79–119 (1988)
Liang, F.M.: A lower bound for on-line bin packing. Inform. Process. Lett. 10, 76–79 (1980)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Comm. of the ACM 28(2), 202–208 (1985)
Zhang, G.: A new version of on-line variable-sized bin packing. Discrete Applied Mathematics 72, 193–197 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Boyar, J., Ellen, F. (2013). Bounds for Scheduling Jobs on Grid Processors. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds) Space-Efficient Data Structures, Streams, and Algorithms. Lecture Notes in Computer Science, vol 8066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40273-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-40273-9_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40272-2
Online ISBN: 978-3-642-40273-9
eBook Packages: Computer ScienceComputer Science (R0)