|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{refimprove|date=August 2012}}
| | You have a objective to lose weight swiftly plus these rapidly weight reduction tips are created to aid we reach that goal. Losing weight quickly will happen for you however, I can warn we that when you are not ready to place forth the effort needed you will not get the results you wish. These strategies might require a effort however, if you have the desire to get the weight off the body now, this short article will show we how.<br><br>Personally, I am amazed at the change in her body beyond the fat reduction. So many persons tell me they cannot receive rid of stomach fat whenever they lose weight, nevertheless Sherry looks incredible! Her healthy weight loss program apparently was precisely what the Doctor ordered to lose weight fast plus healthy.<br><br>January is a hot income for DVD sales, fitness books, and gym memberships, however, what if you could motivate persons by having them bet on their ability to lose weight? There are 3 different companies that will aid we make several funds off a own weight loss.<br><br>Equipment are excellent aids whenever it comes to losing fat. But accessories that goes around a body to target fat burns on specific regions, that's merely TOO GOOD TO BE TRUE. I don't care how superior those models look on tv, it simply defies the odds of human nature. And sometimes they even show we the effects of utilizing them for simply 30 minutes and PRESTO! 2-5 inches (5-10 LBS) just flew off miraculously. I bet we that they wouldn't dare to measure which person again inside 30 minutes, considering the LBS would miraculously FLY BACK!<br><br>Consuming Fruits plus Vegetables: Consuming green leafy greens plus fruits daily can help you detoxify the body and the fat inside the body. They are sometimes known [http://safedietplansforwomen.com/how-to-lose-weight-fast how to lose weight fast] to stimulate the metabolism system which results inside fat reduction. Various sprouted beans, pulses, legumes, fruits and greens, aid we remain full for longer leaving less chances for hogging on the junk.<br><br>Vegan diet is nothing however, a diet that involves just vegetarian foods plus no food items from dead animals. You are able to even frame a diet by oneself by choosing the amount of calories you need to consume in a day. Given below is one such test diet which allows you to consume 1400 calories in a day.<br><br>Please try other treatments plus food guides about eating proper to help you see the right system for you to get rid of weight quick. Here's the link to The Fat Loss Factor website if you would like to test it. |
| The '''assignment problem''' is one of the fundamental [[combinatorial optimization]] problems in the branch of [[Optimization (mathematics)|optimization]] or [[operations research]] in [[mathematics]]. It consists of finding a maximum weight [[Matching (graph theory)|matching]] in a [[weighted graph|weighted]] [[bipartite graph]].
| |
| | |
| In its most general form, the problem is as follows:
| |
| | |
| :There are a number of ''agents'' and a number of ''tasks''. Any agent can be assigned to perform any task, incurring some ''cost'' that may vary depending on the agent-task assignment. It is required to perform all tasks by assigning exactly one agent to each task and exactly one task to each agent in such a way that the ''total cost'' of the assignment is minimized.
| |
| | |
| If the numbers of agents and tasks are equal and the total cost of the assignment for all tasks is equal to the sum of the costs for each agent (or the sum of the costs for each task, which is the same thing in this case), then the problem is called the ''linear assignment problem''. Commonly, when speaking of the ''assignment problem'' without any additional qualification, then the ''linear assignment problem'' is meant.
| |
| | |
| == Algorithms and generalizations ==
| |
| | |
| The [[Hungarian algorithm]] is one of many [[algorithm]]s that have been devised that solve the linear assignment problem within time bounded by a polynomial expression of the number of agents.
| |
| | |
| The assignment problem is a special case of the [[transportation problem]], which is a special case of the [[minimum cost flow problem]], which in turn is a special case of a [[linear program]]. While it is possible to solve any of these problems using the [[simplex algorithm]], each specialization has more efficient algorithms designed to take advantage of its special structure. If the cost function involves quadratic inequalities it is called the [[quadratic assignment problem]].
| |
| | |
| ==Example==
| |
| | |
| Suppose that a taxi firm has three taxis (the agents) available, and three customers (the tasks) wishing to be picked up as soon as possible. The firm prides itself on speedy pickups, so for each taxi the "cost" of picking up a particular customer will depend on the time taken for the taxi to reach the pickup point. The solution to the assignment problem will be whichever combination of taxis and customers results in the least total cost.
| |
| | |
| However, the assignment problem can be made rather more flexible than it first appears. In the above example, suppose that there are four taxis available, but still only three customers. Then a fourth dummy task can be invented, perhaps called "sitting still doing nothing", with a cost of 0 for the taxi assigned to it. The assignment problem can then be solved in the usual way and still give the best solution to the problem.
| |
| | |
| Similar tricks can be played in order to allow more tasks than agents, tasks to which multiple agents must be assigned (for instance, a group of more customers than will fit in one taxi), or maximizing profit rather than minimizing cost.
| |
| | |
| ==Formal mathematical definition==
| |
| | |
| The formal definition of the '''assignment problem''' (or '''linear assignment problem''') is
| |
| | |
| :Given two sets, ''A'' and ''T'', of equal size, together with a [[weight function]] ''C'' : ''A'' × ''T'' → '''[[real number|R]]'''. Find a [[bijection]] ''f'' : ''A'' → ''T'' such that the [[Loss function|cost function]]:
| |
| | |
| ::<math>\sum_{a\in A}C(a,f(a))</math>
| |
| is minimized. | |
| | |
| Usually the weight function is viewed as a square real-valued [[matrix (mathematics)|matrix]] ''C'', so that the cost function is written down as:
| |
| | |
| :<math>\sum_{a\in A}C_{a,f(a)}</math>
| |
| | |
| The problem is "linear" because the cost function to be optimized as well as all the constraints contain only linear terms.
| |
| | |
| The problem can be expressed as a standard [[linear program]] with the objective function
| |
| | |
| :<math>\sum_{i\in A}\sum_{j\in T}C(i,j)x_{ij}</math>
| |
| | |
| subject to the constraints
| |
| | |
| :<math>\sum_{j\in T}x_{ij}=1\text{ for }i\in A, \, </math>
| |
| | |
| :<math>\sum_{i\in A}x_{ij}=1\text{ for }j\in T, \, </math>
| |
| | |
| :<math>x_{ij}\ge 0\text{ for }i,j\in A,T. \, </math>
| |
| | |
| The variable <math>x_{ij}</math> represents the assignment of agent <math>i</math> to task <math>j</math>, taking value 1 if the assignment is done and 0 otherwise. This formulation allows also fractional variable values, but there is always an optimal solution where the variables take integer values. This is because the constraint matrix is [[Unimodular matrix#Total unimodularity|totally unimodular]]. The first constraint requires that every agent is assigned to exactly one task, and the second constraint requires that every task is assigned exactly one agent.
| |
| | |
| ==See also==
| |
| *[[Auction algorithm]]
| |
| *[[Generalized assignment problem]]
| |
| *[[Linear bottleneck assignment problem]]
| |
| *[[National Resident Matching Program]]
| |
| *[[Quadratic assignment problem]]
| |
| *[[Stable marriage problem]]
| |
| *[[Stable roommates problem]]
| |
| *[[Transportation theory (mathematics)|Monge-Kantorovich problem]], a more general formulation
| |
| *[[Weapon target assignment problem]]
| |
| | |
| == Further reading ==
| |
| *{{cite book | last=Brualdi | first=Richard A. | title=Combinatorial matrix classes | series=Encyclopedia of Mathematics and Its Applications | volume=108 | location=Cambridge | publisher=[[Cambridge University Press]] | year=2006 | isbn=0-521-86565-4 | zbl=1106.05001 }}
| |
| * {{cite book | authorlink = Rainer Burkard | first = Rainer | last = Burkard | coauthors = M. Dell'Amico, S. Martello | year = 2012 | title = Assignment Problems (Revised reprint) | publisher = SIAM | isbn = 978-1-61197-222-1 }}
| |
| | |
| [[Category:Combinatorial optimization]]
| |
| [[Category:Matching]]
| |
| [[Category:Polynomial-time problems]]
| |
| [[Category:Linear programming]]
| |
| | |
| [[de:Zuordnungsproblem]]
| |
You have a objective to lose weight swiftly plus these rapidly weight reduction tips are created to aid we reach that goal. Losing weight quickly will happen for you however, I can warn we that when you are not ready to place forth the effort needed you will not get the results you wish. These strategies might require a effort however, if you have the desire to get the weight off the body now, this short article will show we how.
Personally, I am amazed at the change in her body beyond the fat reduction. So many persons tell me they cannot receive rid of stomach fat whenever they lose weight, nevertheless Sherry looks incredible! Her healthy weight loss program apparently was precisely what the Doctor ordered to lose weight fast plus healthy.
January is a hot income for DVD sales, fitness books, and gym memberships, however, what if you could motivate persons by having them bet on their ability to lose weight? There are 3 different companies that will aid we make several funds off a own weight loss.
Equipment are excellent aids whenever it comes to losing fat. But accessories that goes around a body to target fat burns on specific regions, that's merely TOO GOOD TO BE TRUE. I don't care how superior those models look on tv, it simply defies the odds of human nature. And sometimes they even show we the effects of utilizing them for simply 30 minutes and PRESTO! 2-5 inches (5-10 LBS) just flew off miraculously. I bet we that they wouldn't dare to measure which person again inside 30 minutes, considering the LBS would miraculously FLY BACK!
Consuming Fruits plus Vegetables: Consuming green leafy greens plus fruits daily can help you detoxify the body and the fat inside the body. They are sometimes known how to lose weight fast to stimulate the metabolism system which results inside fat reduction. Various sprouted beans, pulses, legumes, fruits and greens, aid we remain full for longer leaving less chances for hogging on the junk.
Vegan diet is nothing however, a diet that involves just vegetarian foods plus no food items from dead animals. You are able to even frame a diet by oneself by choosing the amount of calories you need to consume in a day. Given below is one such test diet which allows you to consume 1400 calories in a day.
Please try other treatments plus food guides about eating proper to help you see the right system for you to get rid of weight quick. Here's the link to The Fat Loss Factor website if you would like to test it.