Abstract
We study a new kind of on-line bin packing, motivated by a problem arising when scheduling jobs on the Grid. In this bin packing problem, the set of items is given at the beginning, and variable-sized bins arrive one by one. We analyze the problem using both the competitive ratio and the relative worst order ratio, observing that the two measures often lead to different conclusions.
A closely related problem was introduced by Zhang (Discrete Appl. Math. 72:193–197, 1997). Our main result answers a question posed in that paper in the affirmative: we give an algorithm with a competitive ratio strictly better than 2, for our problem as well as Zhang’s problem. For identical bins, the new algorithm has essentially the same performance as FFD (First-Fit-Decreasing).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Boyar, J., Ellen, F.: Improved lower bounds for Grid scheduling. Unpublished manuscript (2008)
Boyar, J., Favrholdt, L.M.: The relative worst order ratio for on-line algorithms. In: 5th Italian Conference on Algorithms and Complexity. LNCS, vol. 2653, pp. 58–69. Springer, Berlin (2003). Extended version in ACM Trans. Algorithms 3(2), 22 (2007)
Boyar, J., Medvedev, P.: The relative worst order ratio applied to seat reservation. ACM Trans. Algorithms 4(4), 48 (2008)
Boyar, J., Favrholdt, L.M., Larsen, K.S.: The relative worst order ratio applied to paging. J. Comput. Syst. Sci. 73, 818–843 (2007)
Busch, M.: An investigation of the algorithms for solving the grid scheduling problem (in Danish). Bachelor project, Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark (2006)
Epstein, L., Favrholdt, L.M., Kohrt, J.S.: Separating online scheduling algorithms with the relative worst order ratio. J. Comb. Optim. 12(4), 362–385 (2006)
Garey, M.R., Graham, R.L., Ullman, J.D.: An analysis of some packing algorithms. Combinatorial Algorithms (Courant Computer Science Symposium 9), 39–47 (1972)
Graham, R.L.: Bounds on multiprocessing anomalies and related packing algorithms. In: Proc. 1972 Spring Joint Computer Conference, pp. 205–217 (1972)
Johnson, D.S.: Fast algorithms for bin packing. J. Comput. Syst. Sci. 8, 272–314 (1974)
Kohrt, J.S.: Online algorithms under new assumptions. PhD thesis, Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark (2004)
Karlin, A.R., Manasse, M.S., Rudolph, L., Sleator, D.D.: Competitive snoopy caching. Algorithmica 3(1), 79–119 (1988)
Lee, C., Lee, D.: A simple on-line bin-packing algorithm. J. ACM 32(3), 562–572 (1985)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)
Vinter, B.: Personal communication. http://mig-2.imada.sdu.dk:8092/MiG/Mig/ (2006)
Zhang, G.: A new version of on-line variable-sized bin packing. Discrete Appl. Math. 72, 193–197 (1997)
Author information
Authors and Affiliations
Corresponding author
Additional information
A preliminary version of some of this paper appeared in Algorithm Theory—SWAT 2006, pp. 17–28, 2006.
Supported in part by the Danish Natural Science Research Council (SNF).
Rights and permissions
About this article
Cite this article
Boyar, J., Favrholdt, L.M. Scheduling Jobs on Grid Processors. Algorithmica 57, 819–847 (2010). https://doi.org/10.1007/s00453-008-9257-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00453-008-9257-0