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. Several variants of this problem have been studied.
Rectanglepacking 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...
pack 147 rectangles of size (137,95) in a rectangle of size (1600,1230). Packing different rectangles in a rectangle: The problem of packing multiple...
from 49 onwards. Dense packings of circles in non-square rectangles have also been the subject of investigations. Square packing in a circle Croft, Hallard...
are minimum solutions for n up to 12: Circle packing in a square Squaring the square Rectanglepacking Moving sofa problem Brass, Peter; Moser, William;...
packing in a circle Circle packing in a square Circle packing in a rectangle Circle packing in an equilateral triangle Circle packing in an isosceles right...
Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose...
from bin packing are used in this problem too. In the guillotine cutting problem, both the items and the "bins" are two-dimensional rectangles rather than...
intersection of the universe and geometric shapes (e.g., disks, rectangles). Set packing Maximum coverage problem is to choose at most k sets to cover as...
set packing Minimum edge cover Maximum matching Minimum vertex cover Maximum independent set Bin covering Bin packing Polygon covering Rectanglepacking...
The strip packing problem is a 2-dimensional geometric minimization problem. Given a set of axis-aligned rectangles and a strip of bounded width and infinite...
set packing Minimum edge cover Maximum matching Minimum vertex cover Maximum independent set Bin covering Bin packing Polygon covering Rectanglepacking...
problems and usually integer linear programs, whose dual problems are called packing problems. The most prominent examples of covering problems are the set...
example, the LP relaxations of the set packing problem, the independent set problem, and the matching problem are packing LPs. The LP relaxations of the set...
parity does not prevent a packing, and a packing is indeed possible. It is also possible for two sets of pieces to fit a rectangle of size 420, or for the...
These are variants of the two-dimensional cutting stock, bin packing and rectanglepacking problems, where the cuts are constrained to be guillotine cuts...
of this type are rectangles, and the term axis-aligned rectangle is preferred, although orthogonal rectangle and rectilinear rectangle are in use as well...
of the bin packing problem: in bin covering, the bin sizes are bounded from below and the goal is to maximize their number; in bin packing, the bin sizes...
vertices, with one triangle, one square, and two rectangles meeting at each one. If all the rectangles are themselves square (equivalently, all the edges...
starts with a rectangle partitioned into 2 squares. In each step, a square the length of the rectangle's longest side is added to the rectangle. Since the...
for all cubes of higher dimensions. Square packing in a square Dividing a square into similar rectangles Sprague, R. (1939). "Beispiel einer Zerlegung...
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