In this variant, the small rectangles can have varying lengths and widths, and they should be packed in a given large rectangle. Packing different rectangles in a given rectangle Finding a largest square-packing is NP-hard one may prove this by reducing from 3SAT. A square-packing is equivalent to an independent set in G S. Let G S be the intersection graph of these squares.
Suppose that, for each point p in S, we put a square centered at p. Given a rectilinear polygon (whose sides meet at right angles) R in the plane, a set S of points in R, and a set of identical squares, the goal is to find the largest number of non-overlapping squares that can be packed in points of S. Packing identical squares in a rectilinear polygon As an example result: it is possible to pack 147 small rectangles of size (137,95) in a big rectangle of size (1600,1230). This problem has some applications such as loading of boxes on pallets and, specifically, woodpulp stowage. Common constraints of the problem include limiting small rectangle rotation to 90° multiples and requiring that each small rectangle is orthogonal to the large rectangle. The goal is to pack as many small rectangles as possible into the big rectangle without overlap between any rectangles (small or large). In this variant, there are multiple instances of a single rectangle of size ( l, w), and a bigger rectangle of size ( L, W). Packing identical rectangles in a rectangle Several variants of this problem have been studied. Rectangle packing is a packing problem where the objective is to determine whether a given set of small rectangles can be placed inside a given large polygon, such that no two small rectangles overlap.
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