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Additionally, variants where the shapes are circular or even irregular have been studied. In the latter case, it is referred to as irregular strip packing. Dimension: When not mentioned differently, the strip packing problem is a 2-dimensional problem. However, it also has been studied in three or even more dimensions.
Packing of irregular objects is a problem not lending itself well to closed form solutions; however, the applicability to practical environmental science is quite important. For example, irregularly shaped soil particles pack differently as the sizes and shapes vary, leading to important outcomes for plant species to adapt root formations and ...
A compact binary circle packing with the most similarly sized circles possible. [7] It is also the densest possible packing of discs with this size ratio (ratio of 0.6375559772 with packing fraction (area density) of 0.910683). [8] There are also a range of problems which permit the sizes of the circles to be non-uniform.
Sphere packing finds practical application in the stacking of cannonballs. In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space.
Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle. Table of solutions, 1 ≤ n ≤ 20 [ edit ]
This limitation is overcome in modern algorithms, which can solve to optimality (in the sense of finding solutions with minimum waste) very large instances of the problem (generally larger than encountered in practice [8] [9]). The cutting-stock problem is often highly degenerate, in that multiple solutions with the same amount of waste are ...
Guillotine cutting is a variant of rectangle packing, with the additional constraint that the rectangles in the packing should be separable using only guillotine cuts. Maximum disjoint set (or Maximum independent set ) is a problem in which both the sizes and the locations of the input rectangles are fixed, and the goal is to select a largest ...
Approximation algorithms for bin packing can be classified into two categories: Online heuristics, that consider the items in a given order and place them one by one inside the bins. These heuristics are also applicable to the offline version of this problem. Offline heuristics, that modify the given list of items e.g. by sorting the items by size.