Abstract
We study a variant of online bin packing problem, in which there are two types of bins: (1,1) and (2,R), i.e., unit size bin with cost 1 and size 2 bin with cost R > 1, the objective is to minimize the total cost occurred when all the items are packed into the two types of bins. It is not difficult to see that the offline version of the problem is equivalent to the classical bin packing problem when R > 3. In this paper, we focus on the case R ≤ 3, and propose online algorithms and obtain lower bounds for the problem.
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References
Epstein, L., Levin, A.: An APTAS for Generalized Cost Variable-Sized Bin Packing. SIAM J. Comput. 38(1), 411–428 (2008)
Ullman, J.D.: The performance of a memory allocation algorithm. Technical Report 100, Princeton University, Princeton, NJ (1971)
Johnson, D.S.: Fast algorithm for bin packing. Journal of Computer and System Sciences 8, 272–314 (1974)
Johnson, D.S., Demers, A., Ullman, J.D., Garey, M.R., Graham, R.L.: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J. Comput. 3, 256–278 (1974)
Yao, A.C.C.: New algorithms for bin packing. J. ACM 27, 207–227 (1980)
Coffman, E.G., Garey, M.R., Johnson, D.S.: Approximation algorithms for bin packing: A survey. In: Hochbaum, D. (ed.) Approximation Algorithms. PWS Publishing Company (1997)
Lee, C.C., Lee, D.T.: A simple on-line bin packing algorithm. J. ACM 32(3), 256–278 (1985)
Van Vliet, A.: An improved lower bound for on-line bin packing algorithms. Information Processing Letters 43(5), 277–284 (1992)
Seiden, S.S.: On the online bin packing problem. J. ACM 49, 640–671 (2002)
Seiden, S.S., Van Stee, R., Epstein, L.: New bounds for variable-sized online bin packing. SIAM J. Comput. 32(2), 455–469 (2002)
Friesten, D.K., Langston, M.A.: Variable sized bin packing. SIAM J. Comput. 15, 222–230 (1986)
Kinnerseley, N.G., Langston, M.A.: Online variable-sized bin packing. Discrete Applied Mathematics 22(2), 143–148 (1988)
Csirik, J.: An on-line algorithm for variable-sized bin packing. Acta Informatica 26(8), 697–709 (1989)
Brown, D.J.: A lower bound for on-line one-dimensional bin packing algorithms. Tech. report -864. Coordinated Science Laboratory Urbana IL (1979)
Liang, F.M.: A lower bound for on-line bin packing. Information Processing Letters 10, 76–79 (1980)
Van Vliet, A.: An improved lower bound for online bin packing algorithm. Inform. Process. Lett. 43, 277–284 (1992)
Van Vliet, A.: Lower and upper bounds for online bin packing and scheduling heuristics. Thesis Publishers, Amsterdam (1995)
Blitz, D., Van Vliet, A., Woeginger, G.J.: Lower bounds on the asymptotic worst-case ratio of online bin packing algorithms (1996) (unpublished manuscript)
Valerio de Carvalho, J.M.: LP models for bin packing and cutting stock problem. European Journal of Operational Research 141, 253–273 (2002)
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© 2013 Springer International Publishing Switzerland
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Chen, J., Han, X., Iwama, K., Ting, HF. (2013). Online Bin Packing with (1,1) and (2,R) Bins. In: Widmayer, P., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2013. Lecture Notes in Computer Science, vol 8287. Springer, Cham. https://doi.org/10.1007/978-3-319-03780-6_34
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DOI: https://doi.org/10.1007/978-3-319-03780-6_34
Publisher Name: Springer, Cham
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