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• Bin_packing_problem abstract "In the bin packing problem, objects of different volumes must be packed into a finite number of bins or containers each of volume V in a way that minimizes the number of bins used. In computational complexity theory, it is a combinatorial NP-hard problem. There are many variations of this problem, such as 2D packing, linear packing, packing by weight, packing by cost, and so on. They have many applications, such as filling up containers, loading trucks with weight capacity constraints, creating file backups in media and technology mapping in Field-programmable gate array semiconductor chip design.The bin packing problem can also be seen as a special case of the cutting stock problem. When the number of bins is restricted to 1 and each item is characterised by both a volume and a value, the problem of maximising the value of items that can fit in the bin is known as the knapsack problem.Despite the fact that the bin packing problem has an NP-hard computational complexity, optimal solutions to very large instances of the problem can be produced with sophisticated algorithms. In addition, many heuristics have been developed: for example, the first fit algorithm provides a fast but often non-optimal solution, involving placing each item into the first bin in which it will fit. It requires Θ(n log n) time, where n is the number of elements to be packed. The algorithm can be made much more effective by first sorting the list of elements into decreasing order (sometimes known as the first-fit decreasing algorithm), although this still does not guarantee an optimal solution, and for longer lists may increase the running time of the algorithm. It is known, however, that there always exists at least one ordering of items that allows first-fit to produce an optimal solution.A variant of bin packing that occurs in practice is when items can share space when packed into a bin. Specifically, a set of items could occupy less space when packed together than the sum of their individual sizes. This variant is known as VM packing since when virtual machines (VMs) are packed in a server, their total memory requirement could decrease due to pages shared by the VMs that need only be stored once. If items can share space in arbitrary ways, the bin packing problem is hard to even approximate. However, if the space sharing fits into a hierarchy, as is the case with memory sharing in virtual machines, the bin packing problem can be efficiently approximated.".
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• Bin_packing_problem wikiPageExternalLink vpsolver.
• Bin_packing_problem wikiPageExternalLink citation.cfm?id=3833&jmp=abstract&dl=portal&dl=ACM.
• Bin_packing_problem wikiPageExternalLink BPP.
• Bin_packing_problem wikiPageExternalLink Problems.
• Bin_packing_problem wikiPageExternalLink fpart.
• Bin_packing_problem wikiPageExternalLink www.3dbinpacking.com.
• Bin_packing_problem wikiPageExternalLink erick_dube_507-034.pdf.
• Bin_packing_problem wikiPageExternalLink bin-packing.
• Bin_packing_problem wikiPageExternalLink 74_04_one_dimensional_packing.pdf.
• Bin_packing_problem wikiPageExternalLink www.optaplanner.org.
• Bin_packing_problem wikiPageExternalLink 2027-PHP-Pack-files-without-exceeding-a-given-size-limit.html.
• Bin_packing_problem wikiPageExternalLink solving-packaging-problem-in-php.html.
• Bin_packing_problem wikiPageID "287015".
• Bin_packing_problem wikiPageRevisionID "605065213".
• Bin_packing_problem hasPhotoCollection Bin_packing_problem.
• Bin_packing_problem subject Category:Optimization_algorithms_and_methods.
• Bin_packing_problem subject Category:Packing_problem.
• Bin_packing_problem subject Category:Strongly_NP-complete_problems.
• Bin_packing_problem type Abstraction100002137.
• Bin_packing_problem type Act100030358.
• Bin_packing_problem type Activity100407535.
• Bin_packing_problem type Algorithm105847438.
• Bin_packing_problem type Attribute100024264.
• Bin_packing_problem type Condition113920835.
• Bin_packing_problem type Difficulty114408086.
• Bin_packing_problem type Event100029378.
• Bin_packing_problem type OptimizationAlgorithmsAndMethods.
• Bin_packing_problem type Problem114410605.
• Bin_packing_problem type Procedure101023820.
• Bin_packing_problem type PsychologicalFeature100023100.
• Bin_packing_problem type Rule105846932.
• Bin_packing_problem type State100024720.
• Bin_packing_problem type StronglyNP-completeProblems.
• Bin_packing_problem type YagoPermanentlyLocatedEntity.
• Bin_packing_problem comment "In the bin packing problem, objects of different volumes must be packed into a finite number of bins or containers each of volume V in a way that minimizes the number of bins used. In computational complexity theory, it is a combinatorial NP-hard problem. There are many variations of this problem, such as 2D packing, linear packing, packing by weight, packing by cost, and so on.".
• Bin_packing_problem label "Behälterproblem".
• Bin_packing_problem label "Bin packing problem".
• Bin_packing_problem label "Problème de bin packing".
• Bin_packing_problem label "Задача об упаковке в контейнеры".
• Bin_packing_problem label "ビンパッキング問題".
• Bin_packing_problem label "集装优化".
• Bin_packing_problem sameAs Behälterproblem.
• Bin_packing_problem sameAs Problème_de_bin_packing.
• Bin_packing_problem sameAs ビンパッキング問題.
• Bin_packing_problem sameAs m.01q4sl.
• Bin_packing_problem sameAs Q814581.
• Bin_packing_problem sameAs Q814581.
• Bin_packing_problem sameAs Bin_packing_problem.
• Bin_packing_problem wasDerivedFrom Bin_packing_problem?oldid=605065213.
• Bin_packing_problem isPrimaryTopicOf Bin_packing_problem.