On Lazy Bin Covering and Packing problems

Authors:
Mingen Lin;Yang Yang;Jinhui Xu
Affiliations:
Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA;Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA;Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA
Venue:
Theoretical Computer Science
Year:
2010

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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 prove the approximation ratio of the First-Fit-Decreasing and First-Fit-Increasing algorithms, then present an APTAS. For the online LBC problem, we give a 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 Boyar et al. (2006) [1]. For this problem, we prove that its offline version is no harder to approximate than the offline MRBP problem.