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In mathematics, the packing dimension is one of a number of concepts that can be used to define the dimension of a subset of a metric space.Packing dimension is in some sense dual to Hausdorff dimension, since packing dimension is constructed by "packing" small open balls inside the given subset, whereas Hausdorff dimension is constructed by covering the given subset by such small open balls.
The hexagonal packing of circles on a 2-dimensional Euclidean plane. These problems are mathematically distinct from the ideas in the circle packing theorem.The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere.
In countries that use American paper sizes, a less verifiable measure known as basis weight is used in addition to or instead of grammage. The basis weight of paper is the density of paper expressed in terms of the mass of a ream of given dimensions and a sheet count.
Best-fit is an online algorithm for bin packing.Its input is a list of items of different sizes. Its output is a packing - a partition of the items into bins of fixed capacity, such that the sum of sizes of items in each bin is at most the capacity.
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Dimensional weight, also known as volumetric weight, is a pricing technique for commercial freight transport (including courier and postal services), which uses an estimated weight that is calculated from the length, width and height of a package.
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 sum of non-overlapping rectangles. In contrast, in rectangle packing (as in real-life packing problems) the sizes of the rectangles are given, but their locations are ...
Consider first a special case in which all item sizes are at most 1/2. If there is an FF bin with sum less than 2/3, then the size of all remaining items is more than 1/3. Since the sizes are at most 1/2, all following bins (except maybe the last one) have at least two items, and sum larger than 2/3.
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