Abstract
In this paper, we study two interesting variants of the classical bin packing problem, called Lazy Bin Covering (LBC) and Cardinality Constrained Maximum Resource Bin Packing (CCMRBP) problems. For the offline LBC problem, we first show its NP-hardness, then prove the approximation ratio of the First-Fit-Decreasing algorithm, and finally present an APTAS. For the online LBC problem, we give competitive analysis for the algorithms of Next-Fit, Worst-Fit, First-Fit, and a modified HARMONIC M algorithm. The CCMRBP problem is a generalization of the Maximum Resource Bin Packing (MRBP) problem [1]. For this problem, we prove that its offline version is no harder to approximate than the offline MRBP problem.
This research was partially supported by an NSF CARRER Award CCF-0546509.
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Lin, M., Yang, Y., Xu, J. (2006). On Lazy Bin Covering and Packing Problems. 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_36
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DOI: https://doi.org/10.1007/11809678_36
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