Abstract
We study the multiple-strip packing problem, in which the goal is to pack all the rectangles into m vertical strips of unit widths such that the maximum height among strips used is minimized. A number of on-line algorithms for this problem are proposed, in which the decision of delivering the rectangles to strips as well as packing the rectangles in strips must be done on-line. Both randomized and deterministic on-line algorithms are investigated, and all of them are guaranteed to have constant competitive ratios.
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
Baker, B.S., Coffman, E.G., Rivest, R.L.: Orthogonal Packings in Two Dimensions. SIAM J. Comput. 9, 846–855 (1980)
Baker, B.S., Schwartz, J.S.: Shelf Algorithms for Two-Dimensional Packing Problems. SIAM J. Comput. 12, 508–525 (1983)
Chrobak, M., Kenyon, C., Noga, J., Young, N.: Incremental Medians via Online Bidding. Algorithmica 50(4), 455–478 (2008)
Csirik, J., Woeginger, G.J.: Shelf Algorithms for On-Line Strip Packing. Inform. Process. Lett. 63, 171–175 (1997)
Du, J., Joseph, Y.T.L.: Complexity of Scheduling Parallel Task Systems. SIAM J. Discrete Math. 2, 473–487 (1989)
Foster, I., Kesselman, C.: The Grid: Blueprint for a Future Computing Infrastructure (1999)
Graham, R.L.: Bounds for Certain Multiprocessing Anomalies. Bell System Technical J. 45, 1563–1581 (1966)
Hochbaum, D.S., Shmoys, D.B.: Using Dual Approximation Algorithms for Scheduling Problems: Theoretical and Practical Results. J. ACM 34, 144–162 (1987)
Hurink, J.L., Paulus, J.J.: Online Algorithm for Parallel Job Scheduling and Strip Packing. In: Proc. 5th International Workshop in Approximation and Online Algorithms, pp. 67–74 (2007)
Hurink, J.L., Paulus, J.J.: Online Scheduling of Parallel Jobs on Two Machines is 2-Competitive. Oper. Res. Lett. 36(1), 51–56 (2008)
Marty, M.R., Hill, M.D.: Virtual Hierarchies to Support Server Consolidation. In: Proceedings of the 34th Annual International Conference on Computer Architecture, pp. 46–56 (2007)
Schwiegelshohn, U., Tchernykh, A., Yahyapour, R.: Online Scheduling in Grids. In: IEEE International Symposium on Parallel and Distributed Processing (IPDPS), pp. 1–10 (2008)
Steinberg, A.: A Strip-Packing Algorithm with Absolute Performance Bound 2. SIAM J. Comput. 26, 401–409 (1997)
Ye, D., Han, X., Zhang, G.: A Note on Online Strip Packing. J. Comb. Optim. 17(4), 417–423 (2009)
Ye, D., Zhang, G.: On-Line Scheduling of Parallel Jobs in a List. J. Sched. 10(6), 407–413 (2007)
Zhuk, S.: Approximate Algorithms to Pack Rectangles into Several Strips. Discrete Mathematics and Applications 16(1), 73–85 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ye, D., Han, X., Zhang, G. (2009). On-Line Multiple-Strip Packing. In: Du, DZ., Hu, X., Pardalos, P.M. (eds) Combinatorial Optimization and Applications. COCOA 2009. Lecture Notes in Computer Science, vol 5573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02026-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-02026-1_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02025-4
Online ISBN: 978-3-642-02026-1
eBook Packages: Computer ScienceComputer Science (R0)