Abstract
We study the dynamic bin packing problem introduced by Coffman, Garey and Johnson [7]. This problem is a generalization of the bin packing problem in which items may arrive and depart from the packing dynamically. The main result in this paper is a lower bound of 2.5 on the achievable competitive ratio, improving the best known 2.428 lower bound [3], and revealing that packing items of restricted form like unit fractions (i.e., of size 1/k for some integer k), which can guarantee a competitive ratio 2.4985 [3], is indeed easier.
We also investigate the resource augmentation analysis on the problem where the on-line algorithm can use bins of size b (> 1) times that of the optimal off-line algorithm. An interesting result is that we prove b = 2 is both necessary and sufficient for the on-line algorithm to match the performance of the optimal off-line algorithm, i.e., achieve 1-competitiveness. Further analysis is made to give a trade-off between the bin size multiplier b and the achievable competitive ratio.
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References
Bar-Noy, A., Ladner, R.E., Tamir, T.: Windows scheduling as a restricted version of bin packing. In: Munro, J.I. (ed.) SODA, pp. 224–233. SIAM, Philadelphia (2004)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Chan, W.T., Lam, T.W., Wong, P.W.H.: Dynamic bin packing of unit fractions items. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 614–626. Springer, Heidelberg (2005)
Coffman Jr., E.G., Courcoubetis, C., Garey, M.R., Johnson, D.S., Shor, P.W., Weber, R.R., Yannakakis, M.: Bin packing with discrete item sizes, Part I: Perfect packing theorems and the average case behavior of optimal packings. SIAM J. Discrete Math. 13, 38–402 (2000)
Coffman Jr., E.G., Galambos, G., Martello, S., Vigo, D.: Bin packing approximation algorithms: Combinatorial analysis. In: Du, D.-Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization. Kluwer Academic Publishers, Dordrecht (1998)
Coffman Jr., E.G., Garey, M., Johnson, D.: Bin packing with divisible item sizes. Journal of Complexity 3, 405–428 (1987)
Coffman Jr., E.G., Garey, M.R., Johnson, D.S.: Dynamic bin packing. SIAM J. Comput. 12(2), 227–258 (1983)
Coffman Jr., E.G., Garey, M.R., Johnson, D.S.: Bin packing approximation algorithms: A survey. In: Hochbaum, D.S. (ed.) Approximation Algorithms for NP-Hard Problems, PWS, pp. 46–93 (1996)
Coffman Jr., E.G., Johnson, D.S., McGeoch, L.A., Shor, P.W., Weber, R.R.: Bin packing with discrete item sizes, Part III: Average case behavior of FFD and BFD (in preparation)
Coffman Jr., E.G., Johnson, D.S., Shor, P.W., Weber, R.R.: Bin packing with discrete item sizes, Part II: Tight bounds on first fit. Random Structures and Algorithms 10, 69–101 (1997)
Csirik, J., Woeginger, G.J.: Online packing and covering problems. In: Fiat, A. (ed.) Dagstuhl Seminar 1996. LNCS, vol. 1442, pp. 147–177. Springer, Heidelberg (1998)
Csirik, J., Woeginger, G.J.: Resource augmentation for online bounded space bin packing. J. Algorithms 44(2), 308–320 (2002)
Epstein, L., van Stee, R.: Online bin packing with resource augmentation. In: Persiano, G., Solis-Oba, R. (eds.) WAOA 2004. LNCS, vol. 3351, pp. 23–35. Springer, Heidelberg (2005)
Ivkovic, Z., Lloyd, E.L.: Fully dynamic algorithms for bin packing: Being (mostly) myopic helps. SIAM J. Comput. 28(2), 574–611 (1998)
Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. In: 36th Annual Symposium on Foundations of Computer Science, pp. 214–221 (1995)
Seiden, S.S.: On the online bin packing problem. J. ACM 49(5), 640–671 (2002)
van Vliet, A.: An improved lower bound for on-line bin packing algorithms. Inf. Process. Lett. 43(5), 277–284 (1992)
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Chan, WT., Wong, P.W.H., Yung, F.C.C. (2006). On Dynamic Bin Packing: An Improved Lower Bound and Resource Augmentation Analysis. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_33
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DOI: https://doi.org/10.1007/11809678_33
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