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In the online version of the bin packing problem, the items arrive one after another and the (irreversible) decision where to place an item has to be made before knowing the next item or even if there will be another one.Top 4 Download periodically updates software information of panel cut optimization full versions from the publishers, but some information may be slightly out-of-date. However, this comes at the cost of a (drastically) increased time complexity compared to the heuristical approaches.
They define its decision variant as follows. In Computers and Intractability : 226 Garey and Johnson list the bin packing problem under the reference.
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In contrast, offline bin packing allows rearranging the items in the hope of achieving a better packing once additional items arrive. Here the items of different volume are supposed to arrive sequentially, and the decision maker has to decide whether to select and pack the currently observed item, or else to let it pass. 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.Īnother variant of bin packing of interest in practice is the so-called online bin packing.
If items can share space in arbitrary ways, the bin packing problem is hard to even approximate. 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.
Specifically, a set of items could occupy less space when packed together than the sum of their individual sizes. When the number of bins is restricted to 1 and each item is characterised by both a volume and a value, the problem of maximizing the value of items that can fit in the bin is known as the knapsack problem.Ī variant of bin packing that occurs in practice is when items can share space when packed into a bin. The bin packing problem can also be seen as a special case of the cutting stock problem. There are many variations of this problem, such as 2D packing, linear packing, packing by weight, packing by cost, and so on. It is known, however, that there always exists at least one ordering of items that allows first-fit to produce an optimal solution. The algorithm can be made much more effective by first sorting the list of items 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 requires Θ( n log n) time, where n is the number of items to be packed.
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. In addition, many approximation algorithms exist. Despite its worst-case hardness, optimal solutions to very large instances of the problem can be produced with sophisticated algorithms. The problem has many applications, such as filling up containers, loading trucks with weight capacity constraints, creating file backups in media and technology mapping in FPGA semiconductor chip design.Ĭomputationally, the problem is NP-hard, and the corresponding decision problem - deciding if items can fit into a specified number of bins - is NP-complete. The bin packing problem is an optimization problem, in which items of different sizes must be packed into a finite number of bins or containers, each of a fixed given capacity, in a way that minimizes the number of bins used.