DESCRIPTION:
The container packing problem , the objects must be packed in a finite number of bins of capacity, while minimizing the use of containers.
There many variations of this problem, as in 2D packaging, packaging line, weight, packaging, packing by cost, and so on, it
try to comprehend and make according to the area of \u200b\u200bcontainer declared by me, by calculating the maximum number of items that can be stored safely.
mathematical definition:
V Given the size bin, and a list ... @ n @ 1, sizes of items to pack, find an integer partition AA of
so that
all OPTIMA SOLUTION IF YOU HAVE B-minimum, B-value, to denote an optimal solution OPT.
examples of instances, optimal solutions:
The processing algorithm is in random order, for each object, attempts to place the object in the first bin that can hold the object. If not found bin, open a new folder and puts the object at the beginning again. Get
approximation factor of 2.
DECISION PROBLEM: is impossible for 2 containers of being in the majority of the half. The reason is that if at any time was a hub at most half which means having at least one field of V / 2, the algorithm does not open a new folder for any item whose size is at most V / 2. Only after the tray is filled with more than V / 2 or if an item with a size greater than V / 2 arrives, the algorithm can open a new folder.
You have to check if the object I need to save, rate less than the amount of container space.
OB \u0026lt;= MDE
OB = object, while MDE is defined as half the space of the container.
DECISION ALGORITHM:
estimated if the total dimension of the items is less than or equal to the total dimension of a container.
asking the user the actual amounts, and making transactions with the appropriate functions
Explain the asymptotic complexity :
The asymptotic upper bound is of great importance in computational complexity theory when defining classes complexity.
f (x) = O (g (x)) Although containers (g (x)) is defined as a group, it is customary to write f (x) = O (g (x)) instead of f (x) ∈ O (g (x)). Also often speak of a function by naming only its expression, such as x ² instead of h (x) = x ², provided it is clear which is the parameter of the function within the expression. This graph gives a schematic example of how it behaves cg (x) with respect to f (x) when x tends to infinity.
The tight asymptotic bound (Θ notation) is related to the asymptotic upper and lower bounds (notation Ω):
f (x) = Θ (g (x)) if and only if f (x) = O (g (x)) f (x) = Ω (x)
This means that you can save the maximum amount of items not exceeding the space to use the container.
desicion The problem belongs to P and NP, since
recuersos algorithms, it can do iterative, with a more optimal solution, however, the iterative, recursive can not be made, and involved more aspectors , and instead of making them easier to understand, become more complex, decreasing the simplicity is being sought.
If, NP-complete is the subset of decision problems in NP such that any problem in NP can be reduced in each of the NP-complete problems. You could say that the NP-complete problems are NP hard problems and very likely not part of the complexity class P.
Reason is that to be a polynomial solution for NP-complete problem, all NP problems would also have a solution in polynomial time (and therefore, it is shown that for an NP-complete problem there is no solution in polynomial time, none of the NP problems have a solution).
desicion There are several answers, but what is most effective, is to link the capacity of containers, the space equivalent of items in order not to saturate the container, and use the lowest possible, ie :
That if there is a total sum of items for a minimum number of containers, items can be placed evenly distributed, at the very minimum number of containers?
argue if NP-hard.
is NP-Hard, because there are several ways to find a good solution, but in some cases this is not the best, the optimal solution, using a fitting algorithm, first given the quick fix, but not optimal, putting each item in the container, and if they do not fit elsewhere.
recommend using a heuristic algorithm for this type of problem, because in this way, items are sorted according to volume, and relate to the container space, defining that all containers have the same capacity.
ALGORITHM FOR THE OPTIMIZATION PROBLEM:
Define the dimension of the containers, taking into account that everyone has the same capacity and dimension.
dimension is requested for each item, if it is more than one type of item it
And the number of items to keep,
According to the primary amount of items to keep (by multiplying by the overall dimensions, with a same type), this result is subtracted from the total dimension of a container, if you subtract the space to the container, and there are more items on hold, choose, to fill the entire container, not triple the weight of all items , the weight of the container.
Explain asymptotic complexity of this algorithm as well. Usually Landu notation used to refer to the superiorly bounded functions, which depend on other variables to be true which is defined as:
contenedoresf
A (x) belongs to items (g (x)) when there is a positive constant c such that from a number of articles x0, f (x) does not exceed a container (x). Means that the function f is less aga from a given value except for a constant factor.
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