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Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, people are given: A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers ...
Many techniques from bin packing are used in this problem too. [52] In the guillotine cutting problem, both the items and the "bins" are two-dimensional rectangles rather than one-dimensional numbers, and the items have to be cut from the bin using end-to-end cuts. In the selfish bin packing problem, each item is a player who wants to minimize ...
Printable version; In other projects ... Bin packing (11 P) C. Circle packing (22 P) Pages in category "Packing problems" The following 29 pages are in this category ...
The cutting stock problem is identical to the bin packing problem, but since practical instances usually have far fewer types of items, another formulation is often used. Item j is needed B j times, each "pattern" of items which fit into a single knapsack have a variable, x i (there are m patterns), and pattern i uses item j b ij times:
High-multiplicity bin packing is a special case of the bin packing problem, in which the number of different item-sizes is small, while the number of items with each size is large. While the general bin-packing problem is NP-hard , the high-multiplicity setting can be solved in polynomial time, assuming that the number of different sizes is a ...
First-fit (FF) 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. Ideally, we would like to use as few bins as possible, but minimizing the number of bins ...
A possible placement for the three 1×1×3 blocks – the vertical block has corners touching corners of the two horizontal blocks The solution of the Conway puzzle is straightforward once one realizes, based on parity considerations, that the three 1 × 1 × 3 blocks need to be placed so that precisely one of them appears in each 5 × 5 × 1 slice of the cube. [2]
First-fit-decreasing (FFD) is an algorithm for bin packing. Its input is a list of items of different sizes. 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.