Improved Approximation Algorithms for Maximum Resource Bin Packing and Lazy Bin Covering Problems

摘要

In this paper, we study two variants of the bin packing and covering problems called Maximum Resource Bin Packing (MRBP) and Lazy Bin Covering (LBC) problems, and present new approximation algorithms for them. For the offline MRBP problem, the previous best known approximation ratio is (=1.2) achieved by the classical First-Fit-Increasing (FFI) algorithm (Boyar et al. in Theor. Comput. Sci. 362(1–3):127–139, 2006). In this paper, we give a new FFI-type algorithm with an approximation ratio of (≈1.12676). For the offline LBC problem, it has been shown in Lin et al. (COCOON, pp. 340–349, 2006) that the classical First-Fit-Decreasing (FFD) algorithm achieves an approximation ratio of (≈1.18333). In this paper, we present a new FFD-type algorithm with an approximation ratio of (≈1.13333). Our algorithms are based on a pattern-based technique and a number of other observations. They run in near linear time (i.e., O(nlog n)), and therefore are practical. Keywords Maximum resource bin packing - Lazy bin covering - Approximation algorithms - Pattern The research of this work was supported in part by NSF through CARRER Award CCF-0546509 and grant IIS-0713489. A preliminary version of this paper appeared in the Proceedings of the 17th International Symposium on Algorithms and Computation (ISAAC’06).