Stable Marriage Problem Looked as a Scientific Problem

The fact about stable marriage problem, it is actually a very classic and authoritative science problem in computer. Who in the world does not know what computer is, as they lay on so many places near you. Personal computer are able to be found everywhere. The existence of the personal computer with the addition of word processors, spreadsheets, spelling checkers, and laser printers, has been widely known, even among people who do not consider  themselves as “computer literate”, who care about this kind of electronic. Without us being aware, the occurrence of this technology has changed our everyday life as well.

To make it easier to understand this problem that can be found in the system of computer, the variables are given the set of men and women. Then, the matchmaker will be arranging the marriage in rounds, in where each of the men has to do a proposal to a woman. In return, it is possible for a woman not to get any of the proposals, or one proposal only, or even more than one proposal as well. For example, the case among Bob, Carol, Alice, and Ted. Based on wiki stable marriage problem can be divided into two; the first round is each of the unengaged man proposes to his first preference of the woman, the second one is the possibility that each the woman to reply “maybe” to her admirer, and “no” to all other suitors

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Then with algorithm, the case could be completed. First solved problem would be everyone gets married. Once a woman is engaged to someone, she will always be. Therefore, none of both men and women are unengaged. In the end, the woman has no choice but to say yes. The second guarantee of the algorithm is the stability of marriage. Both Alice and Bob are engaged to another person. If Bob loves Alice more than Carol, then Bon should propose Alice before Carol. The stable of Alice Marriage is seen here; when Alice accepts Bob’s proposal,  yet she does not marry him. When Alice rejects the Bob’s proposal, it means Alice has already with someone she loves the most, more than Bob.

In conclusion, just like other fields, computer science has this recent prospect named object oriented programming. The language of object oriented programming endorses the style of the construction of the program that is called stable marriage problem, which has been described before.

Stable Marriage Problem: a Classic Matching Problem and Algorithm

Stable marriage problem is a problem of classic computer science. In can be found as a problem in mathematics as well. This classical matching problem is first introduced by Gale and Shapely. This problem has the purpose to find a stable matching, especially between two sets of elements that are given a collection of preferences for each elements. This problem is considered as classic because it can be found in the system of computer, and computer is a technology that everybody has been knowing for decades. There assists a polyominal time algorithm to find the solution  of this matching problem.

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If we are studying this matchmaking problem further, we will find this deferred acceptance of stable marriage problem algorithm.

We might reckon a set of women and men, where each of them has a list of some members of their opposite sex as their preference list. The list is ordered. In every process, what is possible to happen is a single man proposes to the the first woman who is listed on his tilt. Yet, the woman has not been proposed by him before. The second case, a woman chooses to reject her current engagement with a man because she prefers to accept the new proposal that she receive from another man. This kind of problem is also known as the men-proposing algorithm.

There are three theorems that can be considered as the completion of that problem of matchmaking, and to make the marriage become stable at the same time. The first theory is the order of proposal of engagement will not affect the stable matching which is made by the men-proposing algorithm. The second theorem is that the matching made by the mentioned men-proposing algorithm is considered as the most stable matching for men. However, on the contrary, it is he most unstable matching for women. This second theorem is called the men-optimal matching. Lastly, the third classical result is in every stable matching, the number of people who remain unengaged is stable or the same.

The structure of proof of this matchmaking problem is divided into three steps. The first step is am algorithm counting the number of the stable man of a given woman. The next step is to bound the possibility of having more than a single stable husband. The last step for this stable marriage problem is to bound the unengaged people by the solution of the occupancy problematic.

Stable Marriage Problem and Its Complexity

Stable marriage problem is a matching problem that is usually found in mathematics or computer science. Meaning, alongside with the mathematics, this matching problem is used in the system of computer as well. This problem, which was first introduced by Gale and Shapely, is very classic. The core of this problem of stable matching is a mapping one set of elements with another set of elements. The problem of stable matching has this instance of men and women, which are considered as unstable if the preference of both a man and a woman are chooses of their own, and are considered stable if they are matched. From this, one can learn about the complexity of this problem.

 

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Here is one example of stable marriage problem complexity. Given you have this n females and n males. Every person has m attributes. Not only that, every person is also indicating an accumulation that a possible candidate—from the given both males and females—should have. Because this problem is a problem of matchmaking, then a matching is considered to have a set of pairs. Every pair has to consist and hold fast a male to a female. The number of attributes that make at least one lucky person satisfied is considered as the satisfaction of a matchmaking. Then, there will occur a question like: is finding a matching with a maximum of satisfactory efficiently solvable? If it was not, then would it be NP-hard?

To solve this problem of complexity, the first step needed is to give a “Satisfaction level” letter k, and question whether there exists a matching in which everyone is matched with the one they have the least k desired attributes with. However, this accomplishment is only about the bipartite matching on a graph in which one can link a male and a female only if they get the satisfaction k from each others. The formula could be written like this; O(MN^2). If you want to return to the avast grade problem, you might do a binary search over k for extra log(m) factor at the moment.

Stable Marriage Problem and Its Completion

Mathematics and computer science are two knowledge that are close to each other, not excluding the share of the same problem, such as the stable marriage problem. This classical problem is known as the problem of matchmaking. Computer is a technology that has been familiar will all of people around the world. It includes the people who consider themselves not a “computer literate”, yet they are aware of this kind of technology. In computer systems, mathematics is needed in order to make the computer works fine. There is a computer program that executing this matching problem, which make this device that can carry out any fine completion of instructions.

Here is a stable marriage problem example which is also the language of computer science. You might consider a set of W for women and M for men, the formula will be |M| = |W| = n. In this case, M x W has all the possible ordered pairs (m, w). Therefore, you will find the problem: given the set of W women and M men and a list of minion for each m Î M and each w Î W. Will there occur a stable matching for each set of minion lists, and if there is one, is it possible for us to construct a stable matching?

If we choose the algorithm to analyze this problem, we will get some answers. First, we are possible to remain engaged since her first offered engagement she received. Her partner she engaged with gets better in terms of her preferences. Secondly, m who proposes a woman can get worse in term of his preferences. To answer the second question, there are some proofs that exist: there is a stable matching for every set of the preference lists. We can do not that each W in women and M in men ranks their own preferences from one to n in a descending order very strictly. The formula will be |M| = |W| = 1. The only pair which is stable is S’, which consist of the pair (m1, w1).

The allegorical problems of this matchmaking is a lot. One of them is called bipartite matching, which is a part of Graph theory. This theory allow us to encounter algorithms in order to solve the general bipartite matching problem, especially the stable marriage problem, when we are studying network flow problems.

Stable Marriage Problem and the Completion with Algorithm

A matchmaking of two elements in mathematics is called stable marriage problem, or SMP. This matchmaking problem is also one of the knowledge of computer science, and firstly introduced by Gale and Shapely. The completion of SMP is used as the computer language. Meanwhile, the completion of this matchmaking SMP is very close to that of a logarithm, because it is the modifications of algorithm itself. Algorithm is a method for computing the SMP. Algorithm itself is taken from the name of a textbook author from Persia, Abu Ja’far Mohamed ibn Musa al-Khowarizmi, the one who found the formula of algebra.

As long as its history, the stable marriage problem algorithm actually precedes the use of computers. It was originally invented in post World War II to match the interns to hospital. In this problem, there is a description on the subject of matching women and men for marriage. A unique assignment will occur when it is given an equal number of both men and women, with a set of preferences for each one of them. In the end the result of this unique assignment will bring happiness. However, there is a problem here: how is it possible to pair up all of them so that there will be no such instabilities?

The core and the idea of this SMP, or problem of matchmaking is to minimise unhappiness, which is very relative. There is no guarantee of how one can be so much better or in contrary so much worse than the others. There exist an information loss, which is caused by the the preference lists are not built by taking the matrix of distance and sorting every row. Meanwhile, a preference list is necessary for this problem. Here are two arrangements that are possible, which are called modulo reflections. These arrangements consist of two pairs in a dimension  .

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This SMP is a part of the system in personal computers to process the user’s demand. Though the technology of computer has been known to all the people around the world, the language of stable marriage is not so popular. Whereas, this solution is a part of the knowledge of mathematics and computer science considered as classical problem which are close to each other. As it is introduced by Gale and Shapely, algorithm is the most necessary way to solve this matchmaking, or stable marriage problem.

Stable Marriage Problem Solution

Providing stable marriage problem has been one of the things that experts are trying to fix nowadays. The number of problematic marriages keeps growing day by day. In fact, there is no marriage which can survive the phantom of the arguments and confrontations, but it is how the couple solves them that matters. Every married couple needs to have a tool box ready to fix the problem of their marriage ready. Solving the rifts and problems that come arise might not be that easy indeed since it is pretty hard to put together two heads as one sometimes.

The number of rifts and problems that a married couple faces are varied. A political interested man probably could not stand the lack of nationalism that his partner has. A middle-aged woman with a high interest in arts probably finds it hard to understand why her husband prefers watching baseball on TV than marveling Picasso in the museum. Simple differences like these often cause a stable marriage problem in a marriage. However, with the right formula, every married couple can overcomes this.
Communication is the oldest yet still effective solution that every expert comes up with when they are asked with the question. Listen actively when your partner opens up about what's bothering his or her mind, but do not interrupt them. Everyone needs to let out a little burden they hold in their shoulder every once in a while with their better half. When an argument is bound to happen, do not yell right away at your partner. Take a time to cool off before going back to talk about it with a level-head. If you like, you might even want to check out the latest invention created by several experts that want to help to solve this old problem with stable marriage problem java. It is probably not the very best choice, but it is probably could help you with your marriage problem better.

With differences turn out to be arguments, some couples find it hard to overcome this problem and patch the rifts quickly. This often causes the separation and divorce cases happened. Many experts still believe in communication as the main solution. If the couples still fail to fix the problems, then it might help to try the algorithms found by experts in a java problem to fix the marriage problem. Nevertheless, it is important to maintain good contact with each other to fix the stable marriage problem that a couple might have.

Stable Marriage Problem: Preventing the Divorce Early

It is important sometimes to find and fix the root of stable marriage problem. Surely every marriage has its own problem, but some problems in some marriages are worse than most. If the two sides of the married couple could not fix this, often times the divorce word is inevitable to come forward as the last solution. In the United States, the number of divorces happened in the 2009 census is no less than 3.4 percent of every 1000 population. Even though it is lower than the previous census, which is 4.1 in 2000, but the number is still staggering.
The causes of the stable marriage problem that eventually cause the divorce are different from one case to another. Some couples confess there was another man or woman outside their married life. Most of the couples that file divorce paper, however, most state “irreconcilable differences” as their reason for divorcing. Some men probably could not stand the burden when their wife has a better career than they. Some women are fed up with their husband who never has the will to improve their economical life. An artsy woman could not stand the political man any longer. A Republic supporter is tired to maintain a supposedly married life with his Democrat supporter's wife. All of these problems might sound stupid to some, but this is actually the fact that happens in real life.

 

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In order to prevent the number to grow back as it is before, or even getting worse, some experts come up with a solution that they think is quite brilliant. They notice that the root of the problems is mostly principal based; so they create an algorithm formed in a form of stable marriage problem c++. This program wants to help the unmarried men and women to find a match that suit them best based on their preferences and likings. Matching the man that prefers x with a woman that also loves the same x is what they believe to be the solution to prevent any unhappy marriage in the future. The same preferences that the couple has been believed to be able to solve and even prevent the heavy confrontations in the future.
With the number of married couple filing divorce paper, the experts come up with the solution. Using a program to prevent the irreconcilable differences from happening, they create an algorithm where a person can meet with their better half. It could be actually the right solution to prevent stable marriage problem happened.