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?
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 .
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.
No comments:
Post a Comment