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The two-dimensional strip packing problem arises in wide variety of industrial applications. In this paper, we focus on the bitmap shape packing problem in which a set of arbitrarily shaped objects represented in bitmap format should be packed into a larger rectangular container without overlap. The complex geometry of bitmap shapes and the large amount of data to be processed make it difficult to check for overlaps. In this paper, we propose an efficient method for checking for overlaps and design efficient implementations of two construction algorithms, which are based on the bottom-left strategy. In this strategy, starting from an empty layout, items are packed into the container one by one. Each item is placed in the lowest position where there is no overlap relative to the current layout. We consider two algorithms, the bottom-left and the best-fit algorithm, which adopt this strategy. The computational results for a series of instances that are generated from well-known benchmark instances show that the proposed algorithms obtain good solutions in remarkably short time and are especially effective for large-scale instances.

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Multilayer films consists of noble metal (Pd, Pt, Cu, Au, PdSi) and transition metal(Co, Ni, PdCo, PtCo, CoZr) layers were prepared by rf sputtering method on glass and/or MgO single crystal substrates. The perpendicular magnetic anisotropy was examined in relation to the magnetostriction, lattice misfits, crystallinity and crystal orientations. The results suggest that the perpendicular magnetic anisotropy in noble metal/PdCo alloy multilayers originates from the magnetoelastic energy of the PdCo layers under a stress due to the lattice misfits. In both Pd/Co and Pd/Ni multilayers, the anisotropy was found to depend on the crystal orientation, and the dependence is discussed from the view point of the magnetoelastic surface anisotropy.

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.