Abstract
The problem of BLASTing a genome against a database of DNA sequences to identify potential relationships with other genomes can be divided into subproblems quite naturally. We consider a setting where the problem is distributed to PCs having idle time. This results in a new variant of bin packing, where a rectangle is divided into smaller rectangles that are to be packed in variable-sized bins which arrive on-line. A rectangle fits in a bin, if the sum of its height and width is no more than the size of the bin. The goal is to minimize the total size of the bins used for packing the entire rectangle.
Simple algorithms exist that work well on small instances of the problem and in the special case where all processors (bins) have the same capacity. We propose an algorithm Slices that works well for more realistic instances in a scenario where the processors vary significantly and arrive on-line.
Similar content being viewed by others
References
Angelopoulos, S., Dorrigiv, R., & López-Ortiz, A. (2007). On the separation and equivalence of paging strategies. In 18th annual ACM-SIAM symposium on discrete algorithms (pp. 229–237).
Ben-David, S., & Borodin, A. (1994). A new measure for the study of on-line algorithms. Algorithmica, 11(1), 73–91.
Borodin, A., & El-Yaniv, R. (1998). Online computation and competitive analysis. London: Cambridge University Press.
Boyar, J., & Favrholdt, L. M. (2007). The relative worst order ratio for on-line algorithms. ACM Transactions on Algorithms, 3(2), 22.
Boyar, J., & Favrholdt, L. M. (2010). Scheduling jobs on Grid processors. Algorithmica, 57(4), 819–847.
Boyar, J., & Medvedev, P. (2008). The relative worst order ratio applied to seat reservation. ACM Transactions on Algorithms, 4(4), 48.
Boyar, J., Favrholdt, L. M., & Larsen, K. S. (2007a). The relative worst-order ratio applied to paging. Journal of Computer and System Sciences, 73, 818–843.
Boyar, J., Ehmsen, M. R., & Larsen, K. S. (2007b). Theoretical evidence for the superiority of LRU-2 over LRU for the paging problem. In LNCS: Vol. 4368. Approximation and online algorithms (WAOA 2006) (pp. 95–107).
Darling, A., Carey, L., & Feng, W. (2003). The design, implementation, and evaluation of mpiBLAST. In ClusterWorld conference & Expo and the 4th international conference on Linux cluster: the HPC revolution 2003.
Ehmsen, M. R., Favrholdt, L. M., Kohrt, J. S., & Mihai, R. (2008). Comparing First-Fit and Next-Fit for online edge coloring. In 19th international symposium on algorithms and computation (pp. 89–99).
Epstein, L., Favrholdt, L. M., & Kohrt, J. S. (2006). Separating scheduling algorithms with the relative worst order ratio. Journal of Combinatorial Optimization, 12(4), 362–385.
Karlin, A. R., Manasse, M. S., Rudolph, L., & Sleator, D. D. (1988). Competitive snoopy caching. Algorithmica, 3(1), 79–119.
Kenyon, C. (1996). Best-fit bin-packing with random order. In 7th annual ACM-SIAM symposium on discrete algorithms (pp. 359–364).
Rangwala, H., Lantz, E., Musselman, R., Pinnow, K., Smith, B., & Wallenfelt, B. (2005). Massively parallel BLAST for the Blue Gene/L. In High availability and performance computing workshop.
Sleator, D. D., & Tarjan, R. E. (1985). Amortized efficiency of list update and paging rules. Communication of the ACM, 28(2), 202–208.
Author information
Authors and Affiliations
Corresponding author
Additional information
Research supported in part by the Danish Agency for Science, Technology and Innovation (FNU).
Rights and permissions
About this article
Cite this article
Boyar, J., Favrholdt, L.M. A new variable-sized bin packing problem. J Sched 15, 273–287 (2012). https://doi.org/10.1007/s10951-010-0199-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-010-0199-4