On lazy bin covering and packing problems

Authors:
Mingen Lin;Yang Yang;Jinhui Xu
Affiliations:
Department of Computer Science and Engineering, University at Buffalo, the State University of New York, Buffalo, NY;Department of Computer Science and Engineering, University at Buffalo, the State University of New York, Buffalo, NY;Department of Computer Science and Engineering, University at Buffalo, the State University of New York, Buffalo, NY
Venue:
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Year:
2006

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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 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.