• 제목/요약/키워드: 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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    • 제14권4호
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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.

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

  • 김현;정태충
    • 전자공학회논문지CI
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    • 제47권6호
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    • pp.68-74
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    • 2010
  • 본 논문에서는 개미의 습성을 연구하여 만들어진 ACS 알고리즘(Ant colony System)을 안정된 결혼문제(SMP: Stable Marriage Problem) 에 적용한 새로운 해결방법을 제시 한다. Gale-Shapley 알고리즘은 안정된 결혼문제(SMP)의 뿌리가 되는 알고리즘으로 오래전부터 실세계에서 연구 및 활용되었다. 본 논문에서 실험의 주제는 같은 수의 남성과 여성을 어떻게 짝을 지어주어야 그들의 선호도를 최대한 반영하여 전체적으로 만족도가 최대가 될 수 있는지를 찾는 것이다. Gale-Shapley 알고리즘은 양성이 아닌 한쪽 성을 중심으로 만족도를 최대화하는 매칭(Matching)을 ��아낼 수 있다. 본 논문에서는 ACS를 적용하여 SMP의 해결을 위한 새로운 해법을 찾아보고자 한다. 이 방법은 남성최적 및 여성최적 뿐만 아니라 양성 최적 및 성균형 최적 매칭을 찾아내는 방법이다. 실험 결과 제안된 방법이 다른 최신의 방법과 비슷한 좋은 결과를 냄을 알 수 있었다.

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

  • 김현;정태충
    • 정보처리학회논문지B
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    • 제18B권3호
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    • pp.165-172
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    • 2011
  • 본 논문에서는 생물학의 개미들이 학습을 통해 목표를 획득하는 방법을 응용한 Ant-Q 알고리즘(Ant Q learning System)[1]을 Gale-Shapley[2]알고리즘을 통해 제시되었던 안정된 결혼문제(SMP: Stable Marriage Problem)[3]의 새로운 해법을 찾기 위해 적용 하였다. SMP는 남성($m_i$)들과 여성($w_j$)들은 각자 자신이 좋아하는 이상형에 대한 선호도(PL: preference list)를 바탕으로 안정이면서도 최선의 짝을 찾는 것을 목표로 하고 있다. Gale-Shapley 알고리즘은 남성(혹은 여성) 위주로 안정적(stability)인 짝(Matching)을 성사시키므로 다양한 조건을 수용하지 못한다. 본 논문에 적용된 Ant-Q는 개미(Ant)의 페로몬을 활용한 학습인 ACS(Ant colony system)에 강화학습의 일종인 Q-학습[9]을 추가한 방법으로, SMP의 새로운 해법을 찾을 수 있었다.

A Marriage Problem Using Threshold Algorithm

  • Lee, Sang-Un
    • 한국컴퓨터정보학회논문지
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    • 제20권11호
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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
    • 대한전자공학회:학술대회논문집
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    • 대한전자공학회 2000년도 ITC-CSCC -2
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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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최대 선호도 순위선정 방법에 기반한 결혼문제 알고리즘 (Marriage Problem Algorithm Based on Maximum-Preferred Rank Selection Method)

  • 이상운
    • 한국인터넷방송통신학회논문지
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    • 제14권3호
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    • pp.111-117
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    • 2014
  • 본 논문은 안정된 결혼문제의 최적 해를 쉽고 빠르게 찾는 알고리즘을 제안하였다. 첫 번째로, 남성의 여성선호도와 여성의 남성 선호도 합 $p_{ij}$$n{\times}n$ 정방행렬 할당문제로 변환시킨다. 두 번째로, 행렬에서 최대 선호도 합(최소 값)인 $_{min}p_{ij}$를 선택하고 i행과 j열을 삭제한다. 이 과정을 $i=0{\cap}j=0$일 때까지 수행한다. 세 번째로, 가능한 최초 또는 마지막 선택 $_{min}p_{ij}$에 대해 다른 값으로 변경시 선호도를 증가시킬 수 있으면 상호 교환하는 검증 절차를 수행한다. 제안된 알고리즘을 7개의 안정된 결혼문제에 적용한 결과 기존 알고리즘의 해를 개선하는 효과를 얻었다.

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

  • 이상운
    • 한국인터넷방송통신학회논문지
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    • 제18권4호
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    • pp.149-154
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    • 2018
  • 안정된 결혼문제에 대해서는 Gale과 Shapley 알고리즘(GSA)이 유일하게 알려져 왔다. 이 알고리즘은 남성이 자신이 가장 선호하는 여성에게 청혼하면 여성이 수락/거절하는 방식(MP)으로 남성 최적-여성 최악의 결과이지만 항상 안정된 매칭 결과를 얻는다. 남성을 여성으로 바꾸어 여성 청혼-남성 수락 방식(WP)을 적용하면 전혀 다른 결과를 얻을 수 있다. 또한 MP나 WP로도 최적의 안정된 매칭 결과를 얻지 못하는 경우도 발생한다. 본 논문에서는 MP와 WP의 이러한 문제점을 해결하기 위해 어떠한 경우라도 최적의 안정된 매칭 결과를 얻는 방법을 제안한다. 제안된 알고리즘은 여성 최악인 MP 결과에 대해 여성을 보상하기 위해 여성이 보다 선호하는 남성들을 대상으로 k명의 여성이 짝을 상호 교환하는 k-opt를 수행하는 방식을 제안하였다. 다양한 사례에 대해 실험을 한 결과 제안된 알고리즘은 MP나 WP로도 얻지 못하는 최적의 안정된 매칭 결과를 얻을 수 있었다.

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

  • 이상운
    • 한국인터넷방송통신학회논문지
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    • 제15권3호
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    • pp.149-154
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    • 2015
  • 본 논문은 안정된 결혼문제의 최적해를 쉽고 빠르게 찾는 알고리즘을 제안하였다. 첫 번째로, 남성의 여성 선호도와 여성의 남성 선호도 합 $p_{ij}$$n{\times}n$ 정방행렬로 변환시킨다. 두 번째로, 행렬에서 최대 반감도 (최악의 선호도)인 최대값 $_{max}p_{ij}$를 행 또는 열의 개수가 1개 ($|r_i|=1$ or $|c_j|=1$)가 존재할 때까지 삭제한다. 만약, $|r_i|=1$ or $|c_j|=1$이면 선택하고, 선택된 $p_{ij}$의 행 또는 열 값을 삭제한다. 이 과정을 ${\forall}(|r_i|=1{\cap}|c_j|=1)$가 될 때까지 반복 수행한다. 제안된 알고리즘을 7개의 안정된 결혼문제에 적용한 결과 간단하면서도 기존 알고리즘의 해를 개선하는 효과를 얻었다.

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

  • 박종렬
    • 디지털융복합연구
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    • 제13권5호
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    • pp.61-67
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    • 2015
  • 정보사회속에 살아가는 무주택서민들의 주거안정을 보장하기 위하여 탄생한 주택임대차보호법은 1981년 3월 5일 법률 제3379호로 민법의 특별법으로 제정되어 2015년 1월 6일까지 15차례의 개정이 있었다. 그동안 수차례에 걸쳐 법률개정으로 인하여 많은 문제점들이 해소된 경우도 있었지만, 입법 당시에 충분한 검토가 없이 졸속으로 처리된 까닭에 시행 후 여러 가지 문제점이 노출되었던 것이 사실이다. 그 중에서 1983년 제1차 개정 시 임차권의 승계규정 제9조를 신설하였던 입법취지는 상속권이 없는 사실혼관계의 배우자에게 승계권을 인정함으로써 사실혼관계 자체를 보호하고, 다른 한편으로는 사실혼관계에 있는 배우자의 주거생활안정을 보호하고자 하였으나, 이에 대해 해석상 여러 가지 의문이 제기되고 있다. 따라서 본 논문에서는 임차권 승계에 대한 문제점을 세밀하게 분석하고, 국민들의 주거생활 안정에 기여하고자 그에 대한 개선방안을 제시하고자 한다.

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

  • 홍종관
    • Clinical and Experimental Reproductive Medicine
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    • 제2권2호
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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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