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 HARMONICM 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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Lin, M., Yang, & Xu, J. (2006). On Lazy Bin Covering and packing problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4112 LNCS, pp. 340–349). Springer Verlag. https://doi.org/10.1007/11809678_36
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