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. 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, and revealing that packing items of restricted form like unit fractions (i.e., of size 1/k for some integer k), for which a 2.4985-competitive algorithm is known, is indeed easier. We also investigate the resource augmentation version of 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 gives a trade-off between the bin size multiplier 1<b≤2 and the achievable competitive ratio.