Improved approximation algorithms for maximum resource bin packing and lazy bin covering 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:
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Year:
2006

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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.