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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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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