An efficient method for checking overlaps and construction algorithms for the bitmap shape packing problem

The two-dimensional strip packing problem arises in wide variety of industrial applications. In this paper, we focus on the bitmap shape packing problem where a set of arbitrary shaped objects represented in bitmap format should be packed into a larger rectangular container without overlap. The complex geometry of bitmap shapes and large amount of data to be processed make it difficult to check overlaps. For this reason, most of the algorithms in the literature only deal with small-scale instances. We propose an efficient method for checking overlaps and design efficient implementations of two construction algorithms, which are based on the bottom-left strategy. The computational results for a series of well-known benchmark instances show that the proposed algorithms obtain good solutions in remarkably short time and are effective for large-scale instances.