On Dynamic Bin Packing: An Improved Lower Bound and Resource Augmentation Analysis

Abstract

We study the dynamic bin packing problem introduced by Coffman, Garey and Johnson [7]. This problem is a generalization of the bin packing problem in which items may arrive and depart from the packing dynamically. The main result in this paper is a lower bound of 2.5 on the achievable competitive ratio, improving the best known 2.428 lower bound [3], and revealing that packing items of restricted form like unit fractions (i.e., of size 1/k for some integer k), which can guarantee a competitive ratio 2.4985 [3], is indeed easier. We also investigate the resource augmentation analysis on the problem where the on-line algorithm can use bins of size b (> 1) times that of the optimal off-line algorithm. An interesting result is that we prove b = 2 is both necessary and sufficient for the on-line algorithm to match the performance of the optimal off-line algorithm, i.e., achieve 1-competitiveness. Further analysis is made to give a trade-off between the bin size multiplier b and the achievable competitive ratio.