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Rectangle packing

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.

Integer programming formulation, Packing identical squares in a rectilinear polygon & Related problems

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Integer programming formulation

Integer linear programBounding-box-netlengthInteger programDualMaximum flow problem
7 related topics

Packing identical squares in a rectilinear polygon

Rectilinear polygonRight anglesIntersection graphIndependent set3SAT
5 related topics

Related problems

Guillotine cuttingMaximum disjoint setCircle packing in a rectangleSquare packing in a squareDe Bruijn's theorem
5 related topics

Packing identical rectangles in a rectangle

OrthogonalWoodpulpStowage
3 related topics

Topics to explore

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Overview

Packing identical rectangles in a rectangle

Packing identical squares in a rectilinear polygon

Packing different rectangles in a given rectangle

Packing different rectangles in a minimum-area rectangle

Integer programming formulation

Related problems

Advanced semantic analysis

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Map overview Semantic statistics

Rectangle packing

Nodes33
Edges32
Triples14
Avg. degree1.94
Density0.060606
Components1

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Rectangle packing

Top relations

related to Integer programming formulation · 4
Rectangle packing → Further, Given, Objective, One
related to Related problems · 4
Rectangle packing → Guillotine, In, Maximum, Some
is a · 1
Rectangle packing → packing problem where the objective is to determine whether a given set of small rectangles can be placed inside a given large polygon

Important terminology Word statistics

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Important terminology

rectangle rectangles problem packing small given displaystyle set 3-partition big fixed relations large polygon variant goal width length solution rotated

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Rectangle packingis apacking problem where the objective is to determine whether a given set of small rectangles can be placed inside a given large polygon0.90text
loading of boxes on pallets andinstance ofmultiples and requiring that each small rectangle is orthogonal to the large rectangle.This problem has some applications0.80text
specificallyinstance ofmultiples and requiring that each small rectangle is orthogonal to the large rectangle.This problem has some applications0.80text
woodpulp stowageinstance ofmultiples and requiring that each small rectangle is orthogonal to the large rectangle.This problem has some applications0.80text
O-treesinstance ofHeuristics Using different representations0.80text
Binstance ofHeuristics Using different representations0.80text
Rectangle packingrelated to Integer programming formulationOne0.60section
Rectangle packingrelated to Integer programming formulationFurther0.60section
Rectangle packingrelated to Integer programming formulationGiven0.60section
Rectangle packingrelated to Integer programming formulationObjective0.60section
Rectangle packingrelated to Related problemsGuillotine0.60section
Rectangle packingrelated to Related problemsMaximum0.60section

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    Min side: 3
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