Scheduling Jobs on Grid Processors
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).
KeywordsGrid scheduling problem Zhang’s bin packing problem On-line algorithms First-Fit-Decreasing
Unable to display preview. Download preview PDF.
- 1.Boyar, J., Ellen, F.: Improved lower bounds for Grid scheduling. Unpublished manuscript (2008) Google Scholar
- 2.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) Google Scholar
- 5.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) Google Scholar
- 7.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) Google Scholar
- 8.Graham, R.L.: Bounds on multiprocessing anomalies and related packing algorithms. In: Proc. 1972 Spring Joint Computer Conference, pp. 205–217 (1972) Google Scholar
- 10.Kohrt, J.S.: Online algorithms under new assumptions. PhD thesis, Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark (2004) Google Scholar
- 14.Vinter, B.: Personal communication. http://mig-2.imada.sdu.dk:8092/MiG/Mig/ (2006)