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.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-642-02026-1_14
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