An Improved Online Multidimensional Bin Packing Algorithm

Abstract

As a fundamental optimization problem, the problem of packing a given set of objects into the fewest possible bins has both important theoretical significance in algorithms and operations research and great application values for resource allocation, particularly in cloud computing and data center management. In this paper we address the multidimensional online bin packing problem and present an algorithm based on the ROUNDdM algorithm proposed by Csirik & Van Vliet [6]. The ROUNDdM algorithm is a generalisation of the harmonic partitioning scheme in [7], and guarantees a worst case approximation ratio of 1.691d for d-dimensions and an average case ratio of 1.2899d. Our HYBRID-ROUNDdM algorithm uses a harmonic based hybrid partitioning scheme and improves this average case approximation ratio to 1.0797d while guaranteeing the same worst case approximation ratio.