• Title/Summary/Keyword: Stable Marriage Problem

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A New Perspective to Stable Marriage Problem in Profit Maximization of Matrimonial Websites

  • Bhatnagar, Aniket;Gambhir, Varun;Thakur, Manish Kumar
    • Journal of Information Processing Systems
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    • v.14 no.4
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    • pp.961-979
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    • 2018
  • For many years, matching in a bipartite graph has been widely used in various assignment problems, such as stable marriage problem (SMP). As an application of bipartite matching, the problem of stable marriage is defined over equally sized sets of men and women to identify a stable matching in which each person is assigned a partner of opposite gender according to their preferences. The classical SMP proposed by Gale and Shapley uses preference lists for each individual (men and women) which are infeasible in real world applications for a large populace of men and women such as matrimonial websites. In this paper, we have proposed an enhancement to the SMP by computing a weighted score for the users registered at matrimonial websites. The proposed enhancement has been formulated into profit maximization of matrimonial websites in terms of their ability to provide a suitable match for the users. The proposed formulation to maximize the profits of matrimonial websites leads to a combinatorial optimization problem. We have proposed greedy and genetic algorithm based approaches to solve the proposed optimization problem. We have shown that the proposed genetic algorithm based approaches outperform the existing Gale-Shapley algorithm on the dataset crawled from matrimonial websites.

Solution of SMP Problem by Adapting ACS Algorithm (ACS알고리즘을 이용한 안정된 결혼 문제 해결에 관한 연구)

  • Kim, Hyun;Chung, Tae-Choong
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.47 no.6
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    • pp.68-74
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    • 2010
  • This paper suggest a new ACS algorithm to solve SMP which was solved by Gale-Shapley algorithm. The stable marriage problem is an extensively-studied combinatorial problem with many practical applications. The classical Gale-Shapley algorithm produces a marriage that greatly favors the men at the expense of the women, or vice versa. In this paper we apply ACS algorithm to SMP to find 4 kinds of solutions such as stable matching with man-optimal, woman-optimal, egalitarian stable matching, sex-fair stable matching. So this ACS is a novel method to solve Stable Marriage Problem. Our simulation results show the effectiveness of the proposed ACS.

Solving the Gale-Shapley Problem by Ant-Q learning (Ant-Q 학습을 이용한 Gale-Shapley 문제 해결에 관한 연구)

  • Kim, Hyun;Chung, Tae-Choong
    • The KIPS Transactions:PartB
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    • v.18B no.3
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    • pp.165-172
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    • 2011
  • In this paper, we propose Ant-Q learning Algorithm[1], which uses the habits of biological ants, to find a new way to solve Stable Marriage Problem(SMP)[3] presented by Gale-Shapley[2]. The issue of SMP is to find optimum matching for a stable marriage based on their preference lists (PL). The problem of Gale-Shapley algorithm is to get a stable matching for only male (or female). We propose other way to satisfy various requirements for SMP. ACS(Ant colony system) is an swarm intelligence method to find optimal solution by using phermone of ants. We try to improve ACS technique by adding Q learning[9] concept. This Ant-Q method can solve SMP problem for various requirements. The experiment results shows the proposed method is good for the problem.

A Marriage Problem Using Threshold Algorithm

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.20 no.11
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    • pp.105-110
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    • 2015
  • This paper deals with a newly proposed algorithm for stable marriage problem, which I coin threshold algorithm. The proposed algorithm firstly constructs an $n{\times}n$ matrix of the sum of each sex's preference over the members of the opposite sex. It then selects the minimum value from each row and column to designate the maximum value of the selected as the sum threshold $p^*_{ij}$. It subsequently deletes the maximum preference $_{mzx}p_{ij}$ from a matrix derived from deleting $p_{ij}$ > $p^*_{ij}$, until ${\mid}c_i{\mid}=1$ or ${\mid}c_j{\mid}=1$. Finally, it undergoes an optimization process in which the sum preference is minimized. When tested on 7 stable marriage problems, the proposed algorithm has proved to improve on the existing solutions.

Stabilizing Unstable Matching because of a Varied Preference List in Distributed Stable Marriage Problem

  • Kinjo, Hideki;Nakamura, Morikazu;Onaga, Kenji
    • Proceedings of the IEEK Conference
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    • 2000.07b
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    • pp.1033-1036
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    • 2000
  • A distributed stable marriage problem in extended in this paper. The traditional approach related to the stable matching problem assume that preference lists are fixed. However, in decentralized version this assumption is not reasonable because of the autonomy of members. In this paper, we consider the situation that a preference list can be varied at some stable matching and show the condition to be broken the stability of the original matching. Moreover, we propose a stabilization algorithm to obtain a stable matching by execution with a minimal set of members.

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Marriage Problem Algorithm Based on Maximum-Preferred Rank Selection Method (최대 선호도 순위선정 방법에 기반한 결혼문제 알고리즘)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.14 no.3
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    • pp.111-117
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    • 2014
  • In this paper I propose a simple optimal solution seeking algorithm to a stable marriage problem. The proposed algorithm firstly constructs an $n{\times}n$ matrix of the sum of each gender's preference of the other gender $p_{ij}$. It then selects the minimum sum preference $_{min}p_{ij}$ in the constructed matrix and deletes its corresponding row i and column j. This process is repeated until $i=0{\cap}j=0$, after which the algorithm compares initially or last chosen $_{min}p_{ij}$ its alternatives to finally determine one that yields the maximum marginal increase in preference. When applied to 7 stable marriage problems, the proposed algorithm has improved on initial solutions of existing algorithms.

An Optimal Algorithm for Stable Marriage Problem (안정된 결혼문제에 대한 최적화 알고리즘)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.18 no.4
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    • pp.149-154
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    • 2018
  • There is well known algorithm is a Gale-Shapley algorithm(GSA) for stable marriage problem. The GSA is performed as each man propose to his most favorite woman(MP), then the woman accepts more than one proposal rejects all but her favorite from among those who have proposed to her. This algorithm always gets a stable set of marriages with man-optimal and woman-pessimal. But the woman proposal and man-accept/reject method(WP) is can be get the distinct result. Also, the optimal stable matching may be fail using MP or WP. This paper suggests always get the optimal stable matching on all occasions in order to overcome the shortcomings of MP and WP. The proposed algorithm perform k-opt, k-women exchange with each other for the result of delete at less preference in each woman from MP result. As a result of applied to various experimental data, this algorithm can be get the optimal stable matching that the MP or WP failed to it.

Marriage Problem Algorithm based on the Maximum Dispreference Sum-Delete Method (최대 반감도 합-삭제 방법에 기반한 결혼문제 알고리즘)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.15 no.3
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    • pp.149-154
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    • 2015
  • In this paper proposes a stable marriage algorithm. The proposed algorithm firstly constructs an $n{\times}n$ matrix of men's and women's sum preference over opposite sex $p_{ij}$. It then repeatedly deletes row or column corresponding to the then maximum dispreference sum $_{max}p_{ij}$ until ${\forall}(|r_i|=1{\cap}|c_j|=1)$. If $|r_i|=1$ or $|c_j|=1$ then we select the $p_{ij}$ of $|r_i|=1$ or $|c_j|=1$ then the row or column values are deleted repeatedly until ${\forall}(|r_i|=1{\cap}|c_j|=1)$. When tested on 7 stable marriage problems, the proposed algorithm has proved to improve on the existing solutions.

The Improvement and Problem about Housing Lease Protection Act Article 9 in the Information Society (정보사회에 있어서 주택임대차보호법 제9조의 문제점에 대한 개선방안)

  • Park, Jong-Ryeol
    • Journal of Digital Convergence
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    • v.13 no.5
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    • pp.61-67
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    • 2015
  • In order to ensure the housing stability of homeless people who living in the information society, the Korean Housing Lease Protection Act was enacted as a special law of Civil Code in March 5, 1981, Law No. 3379. And until January 6, 2015 there were 15 times revisions. In the meantime, many issues have been resolved by legal revisions through several times however, it is true that many problems are exposed after enforcement because processing without sufficient review of legislation. Among them, at the 1st revision in 1983 the purpose of Article 9 for lease succession was admitting succession to a spouse who has no inheritance rights. Then it can protect common-law relationship and on the other hand protect the residential life of a spouse. But many questions have been raised. Therefore, in this paper, analyze the problem of lease succession carefully, proposes an improvement to contribute to the residential stable livelihood.

Problems in the Korean National Family Planning Program (한국가족계획사업(韓國家族計劃事業)의 문제점(問題點))

  • Hong, Jong-Kwan
    • Clinical and Experimental Reproductive Medicine
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    • v.2 no.2
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    • pp.27-36
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    • 1975
  • The success of the family planning program in Korea is reflected in the decrease in the growth rate from 3.0% in 1962 to 2.0% in 1971, and in the decrease in the fertility rate from 43/1,000 in 1960 to 29/1,000 in 1970. However, it would be erroneous to attribute these reductions entirely to the family planning program. Other socio-economic factors, such as the increasing age at marriage and the increasing use of induced abortions, definitely had an impact on the lowered growth and fertility rate. Despite the relative success of the program to data in meeting its goals, there is no room for complacency. Meeting the goal of a further reduction in the population growth rate to 1.3% by 1981 is a much more difficult task than any one faced in the past. Not only must fertility be lowered further, but the size of the target population itself will expand tremendously in the late seventies; due to the post-war baby boom of the 1950's reaching reproductive ages. Furthermore, it is doubtful that the age at marriage will continue to rise as in the past or that the incidence of induced abortion will continue to increase. Consequently, future reductions in fertility will be more dependent on the performance of the national family planning program, with less assistance from these non-program factors. This paper will describe various approaches to help to the solution of these current problems. 1. PRACTICE RATE IN FAMILY PLANNING In 1973, the attitude (approval) and knowledge rates were quite high; 94% and 98% respectively. But a large gap exists between that and the actual practice rate, which is only 3695. Two factors must be considered in attempting to close the KAP-gap. The first is to change social norms, which still favor a larger family, increasing the practice rate cannot be done very quickly. The second point to consider is that the family planning program has not yet reached all the eligible women. A 1973 study determineded that a large portion, 3096 in fact, of all eligible women do not want more children, but are not practicing family planning. Thus, future efforts to help close the KAP-gap must focus attention and services on this important large group of potential acceptors. 2. CONTINUATION RATES Dissatisfaction with the loop and pill has resulted in high discontinuation rates. For example, a 1973 survey revealed that within the first six months initial loop acceptance. nearly 50% were dropouts, and that within the first four months of inital pill acceptance. nearly 50% were dropouts. These discontinuation rates have risen over the past few years. The high rate of discontinuance obviously decreases the contraceptive effectiveness. and has resulted in many unwanted births which is directly related to the increase of induced abortions. In the future, the family planning program must emphasize the improved quality of initial and follow-up services. rather than more quantity, in order to insure higher continuation rates and thus more effective contraceptive protection. 3. INDUCED ABORTION As noted earlier. the use of induced abortions has been increase yearly. For example, in 1960, the average number of abortions was 0.6 abortions per women in the 15-44 age range. By 1970. that had increased to 2 abortions per women. In 1966. 13% of all women between 15-44 had experienced at least one abortion. By 1971, that figure jumped to 28%. In 1973 alone, the total number of abortions was 400,000. Besides the ever incre.sing number of induced abortions, another change has that those who use abortions have shifted since 1965 to include- not. only the middle class, but also rural and low-income women. In the future. in response to the demand for abortion services among rural and low-income w~men, the government must provide and support abortion services for these women as a part of the national family planning program. 4. TARGET SYSTIi:M Since 1962, the nationwide target system has been used to set a target for each method, and the target number of acceptors is then apportioned out to various sub-areas according to the number of eligible couples in each area. Because these targets are set without consideration for demographic factors, particular tastes, prejudices, and previous patterns of acceptance in the area, a high discontinuation rate for all methods and a high wastage rate for the oral pill and condom results. In the future. to alleviate these problems of the methodbased target system. an alternative. such as the weighted-credit system, should be adopted on a nation wide basis. In this system. each contraceptive method is. assigned a specific number of points based upon the couple-years of protection (CYP) provided by the method. and no specific targets for each method are given. 5. INCREASE OF STERILIZA.TION TARGET Two special projects. the hospital-based family planning program and the armed forces program, has greatly contributed to the increasing acceptance in female and male sterilization respectively. From January-September 1974, 28,773 sterilizations were performed. During the same time in 1975, 46,894 were performed; a 63% increase. If this trend continues, by the end of 1975. approximately 70,000 sterilizations will have been performed. Sterilization is a much better method than both the loop and pill, in terms of more effective contraceptive protection and the almost zero dropout rate. In the future, the. family planning program should continue to stress the special programs which make more sterilizations possible. In particular, it should seek to add the laparoscope techniques to facilitate female sterilization acceptance rates. 6. INCREASE NUMBER OF PRIVATE ACCEPTORS Among the current family planning users, approximately 1/3 are in the private sector and thus do not- require government subsidy. The number of private acceptors increases with increasing urbanization and economic growth. To speed this process, the government initiated the special hospital based family planning program which is utilized mostly by the private sector. However, in the future, to further hasten the increase of private acceptors, the government should encourage doctors in private practice to provide family planning services, and provide the contraceptive supplies. This way, those do utilize the private medical system will also be able to receive family planning services and pay for it. Another means of increasing the number of private acceptors, IS to greatly expand the commercial outlets for pills and condoms beyond the existing service points of drugstores, hospitals, and health centers. 7. IE&C PROGRAM The current preferred family size is nearly twice as high as needed to achieve a stable poplation. Also, a strong boy preference hinders a small family size as nearly all couples fuel they must have at least one or more sons. The IE&C program must, in the future, strive to emphasize the values of the small family and equality of the sexes. A second problem for the IE&C program to work. with in the: future is the large group of people who approves family planning, want no more children, but do not practice. The IE&C program must work to motivate these people to accept family planning And finally, for those who already practice, an IE&C program in the future must stress continuation of use. The IE&C campaign, to insure highest effectiveness, should be based on a detailed factor analysis of contraceptive discontinuance. In conclusion, Korea faces a serious unfavorable sociodemographic situation- in the future unless the population growth rate can be curtailed. And in the future, the decrease in fertility will depend solely on the family planning program, as the effect of other socio-economic factors has already been maximumally felt. A second serious factor to consider is the increasing number of eligible women due to the 1950's baby boom. Thus, to meet these challenges, the program target must be increased and the program must improve the effectiveness of its current activities and develop new programs.

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