Abstract
In this paper, we study two variants of the bin packing /covering problems called Maximum Resource Bin Packing (MRBP) and Lazy Bin Covering (LBC) problems, and present new approximation algorithms for each of them. For the offline MRBP problem, the previous best known approximation ratio is \(\frac{6}{5}=1.2\), achieved by the classical First-Fit-Increasing (FFI) algorithm [1]. In this paper, we give a new FFI-type algorithm with an approximation ratio of \(\frac{80}{71}\approx 1.12676\). For the offline LBC problem, it has been shown in [2] that the classical First-Fit-Decreasing (FFD) algorithm achieves an approximation ratio of \(\frac{71}{60}\approx 1.18333\). In this paper, we present a new FFD-type algorithm with an approximation ratio of \(\frac{17}{15}\approx 1.13333\). Both algorithms are simple, run in near linear time (i.e., O(n logn)), and therefore are practical.
The research of this work was supported in part by an NSF CARRER Award CCF-0546509.
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References
Boyar, J., Epstein, L., Favrholdt, L.M., Kohrt, J.S., Larsen, K.S., Pedersen, M.M., Wøhlk, S.: The maximum resource bin packing problem. In: Liśkiewicz, M., Reischuk, R. (eds.) FCT 2005. LNCS, vol. 3623, pp. 397–408. Springer, Heidelberg (2005)
Lin, M., Yang, Y., Xu, J.: On lazy bin covering and packing problems. In: Chen, D.Z., Lee, D.T. (eds.) COCOON 2006. LNCS, vol. 4112, Springer, Heidelberg (2006)
Garey, M.R., Graham, R.L., Johnson, D.S.: Resource constrained scheduling as generalized bin packing. J. Comb. Theory, Ser. A 21, 257–298 (1976)
Csirik, J.: The parametric behavior of the first-fit decreasing bin packing algorithm. J. Algorithms 15, 1–28 (1993)
Csirik, J., Johnson, D.S.: Bounded space on-line bin packing: Best is better than first. Algorithmica 31, 115–138 (2001)
Johnson, D.S., Garey, M.R.: A 71/60 theorem for bin packing. J. Complexity 1, 65–106 (1985)
Galambos, G., Woeginger, G.: Repacking helps in bounded space on-line bin-packing. Computing 49, 329–338 (1993)
Woeginger, G.J.: Improved space for bounded-space, on-line bin-packing. SIAM J. Discrete Math. 6, 575–581 (1993)
Shachnai, H., Tamir, T.: On two class-constrained versions of the multiple knapsack problem. Algorithmica 29, 442–467 (2001)
Friesen, D.K., Langston, M.A.: Analysis of a compound bin packing algorithm. SIAM J. Discrete Math. 4, 61–79 (1991)
Bar-Noy, A., Ladner, R.E., Tamir, T.: Windows scheduling as a restricted version of bin packing. In: SODA 2004, pp. 224–233 (2004)
Csirik, J., Kenyon, C., Johnson, D.S.: Better approximation algorithms for bin covering. In: SODA, pp. 557–566 (2001)
Assmann, S.F., Johnson, D.S., Kleitman, D.J., Leung, J.Y.T.: On a dual version of the one-dimensional bin packing problem. J. Algorithms 5, 502–525 (1984)
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Lin, M., Yang, Y., Xu, J. (2006). Improved Approximation Algorithms for Maximum Resource Bin Packing and Lazy Bin Covering Problems. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_57
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DOI: https://doi.org/10.1007/11940128_57
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