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	The Stable Marriage Problem
		The Stable Marriage problem is a classical combinatorial problem that belongs to the family of stable matching problems.
		It is known that every instance of the Stable Marriage problem admits at least one stable matching, and furthermore, such a matching can be found in time linear in the size of the problem instance using an efficient algorithm known as the Gale/Shapley algorithm [1].
		The user is prompted to enter the number n of men in a given instance of the Stable Marriage problem (n must be between 1 and 16).
	www.dcs.gla.ac.uk /research/algorithms/stable/EGSapplet/intro.html (267 words)

	PlanetMath: stable marriage problem
		The stable marriage problem is to determine whether all people can be married with all marriages stable.
		Hence both marriages are stable: each woman is either satisfied with her marriage or is unable to find a man willing to have an affair.
		This is version 2 of stable marriage problem, born on 2006-08-16, modified 2006-08-16.
	planetmath.org /encyclopedia/Stable2.html (522 words)

	CS W1007 Stable Marriage
		The search for an ideal marriage turns out to be a very appropriate and motiviating setting for discussing many computational issues that are at the intellectual heart of computer science, with interesting connections to the commercial world of computers, and even to the politics of health care.
		Here is the problem of stable marriage: Imagine you are a matchmaker, with one hundred female clients, and one hundred male clients.
		The stable marriage algorithm was described in terms of a matchmaker instructing a group of men and women to act according to a certain set of rules, like a playwright instructing actors in a piece of theatre.
	www1.cs.columbia.edu /~evs/intro/stable/writeup.html (3536 words)

	Stable marriage problem - Wikipedia, the free encyclopedia
		The marriages are stable: Let Alice be a woman and Bob be a man. They are each paired/partnered/married, but not to each other.
		We say that the marriage between man A and woman B is feasible if there exists a stable pairing in which A and B are married.
		The weighted matching problem is to find a matching in a weighted bipartite graph that has maximum weight.
	en.wikipedia.org /wiki/Stable_marriage_problem (873 words)

	The Marriage Problem
		The Bush administration's current marriage initiative-adding a marriage education component to welfare reform-while serving currently as the major "public policy face" of the marriage movement, is quite modest in its scope, relevant only to a tiny fraction of the American adult population, and not currently able to win broad political support in Congress.
		Intellectually, the marriage movement seems to be running out of gas-lacking fresh ideas and especially lacking a broadly shared understanding of the public policy, intellectual, civic, and cultural contests that the marriage movement should seek out, and seek to win, in the coming decade.
		To respond intellectually to the new critics of "the case for marriage," whose emerging argument appears to be that, while happy marriages are beneficial, troubled or unhappy marriages are not, especially for women.
	www.propositionsonline.com /html/the_marriage_problem.html (2865 words)

	Feature Column from the AMS
		The connection with marriage theorems is that one can think of the sets as being the names that each woman lists for the men (who are the elements of the set M, which explains the use of the letter M) whom she would accept as a mate.
		This leads to problems of matching workers to jobs to maximize something (perhaps the efficiency with which all the jobs can be completed) or minimize something (the cost of completing the jobs with a particular assignment of workers).
		Roth, Alvin E. The college admissions problem is not equivalent to the marriage problem.
	www.ams.org /featurecolumn/archive/marriage.html (4234 words)

	[No title]
		This program is an implementation of the standard Stable Marriage problem, written by Chuck Connell in December 2007, for COMP 160 Algorithms at Tufts University.
		Background about the Stable Marriage Problem (SMP) -------------------------------------------------- The Stable Marriage problem is to match a set of men and women with each other, so that no two pairings are "unstable".
		SMP is interesting because it applies to many more situations than fictitious marriages.
	www.chc-3.com /downloads/readme_smp.txt (907 words)

	An Ant Colony Optimization Algorithm for the Stable Roommates Problem
		One NP complete problem that could exploit the ant’s natural behavior is the Stable Roommates Problem.
		The stable roommates problem remains an NP complete problem because instead of having two separate sets, the stable roommate problem is built on a completely connected graph, which contains more edges than a bipartite graph (see Figure 2).
		Once the similarity has been determined, then the problem has been set up and is ready for traversal by the ants from each colony/roommate.
	www.cs.earlham.edu /~uptongl/project/senior_thesis.html (2394 words)

	Michael Williams -- Master of None: The Stable Marriage Problem (Site not responding. Last check: )
		The Marriage Problem is defined as follows: two equal-sized sets of people, male and female, need to form pairs.
		A stable marriage is a set of matchings between these men and women such that, for any given man, there is no woman he prefers over his mate that also prefers him over her mate.
		Nevertheless, stable marriages are theoretically guaranteed as long as the initial conditions are met.
	www.mwilliams.info /archives/003360.php (1713 words)

	A “Fair” Stable Marriage « Jiajin’s TCS Notes
		In this SODA ‘08 paper, they studied the problem of sampling stable matchings in the variants of stable marriage problem.
		Since some instances of stable marriage problem do not have such stable matchings (one can find instances only have man and woman optimal matchings), we hope we can have a random sampling procedure to achieve the fairness in a expected sense.
		It is known that all the stable matchings of a stable marriage problem instance forms a distributive lattice.
	jiajinyu.wordpress.com /2008/05/05/a-fair-stable-marriage (391 words)

	Math Forum: Rubric - Coding DMPoW Problem Difficulty
		Coding of problem difficulty focuses on the mathematical challenges represented by the problem, the difficulty of the mathematical concept, and the difficulty of mathematical calculations for students at a given level of problem solving.
		In this problem, there is only one concept that needs to be worked on, finding the shortest round trip for the mother to complete her errands.
		This problem is based on the Stable Marriage Algorithm, which requires students to make the best match possible between a set of girls and a set of boys desiring to date each other.
	mathforum.org /library/problems/sets/discrete_difficulty.html (791 words)

	ISMP 2000 - Meeting Topics (Site not responding. Last check: )
		Network flow and matching problems are studied from the view of balanced flownetworks: We prove equivalence of the minimum cost balanced circulation problem (MCBCP) with the capacitated $b$-matching problem.
		The proof consists of a reduction to the capacitated $b$-matching problem which in turn is reduced to the $b$-matching problem.
		For a stable marriage problem there is a stable marriage solution inwhich every person is assigned to a partner who is the median partner among all his or her possible mates (Teo-Sethuraman(1998)).
	www.isye.gatech.edu /ismp2000/schedule/session_pages/WEB-04-IC207.html (387 words)

	Stability in Labour Market Games
		Stability ensures that a matching cannot be undermined by two people who could form a private arrangement to their mutual benefit.
		Their algorithm is as amusing as the problem name, since it simulates a courtship process between the men and women.
		We therefore close with the following problem linking classical stability and exchange-stability: it is an open question as to whether the problem of finding a stable matching that is man-exchange-stable is solvable in polynomial time.
	www.ercim.org /publication/Ercim_News/enw57/manlove.html (844 words)

	MTech Thesis Abstract - 9711111
		Stable Marriage problem is a classical problem in matching theory.
		We address a stable marriage problem where each of the persons have equal favour at the time of assignment.
		Given a graph G with n vertices, we can construct an instance of stable marriage problem, such that each solution to the stable marriage will correspond to a solution to the vertex cover in the original graph.
	www.cse.iitk.ac.in /research/mtech1997/9711111.html (131 words)

	3837 - The Stable Marriage Problem
		The stable marriage problem consists of matching members of two different sets according to the member's preferences for the other set's members.
		A marriage is a one-to-one mapping between males and females.
		For each test case find and print the pairs of the stable marriage, which is male-optimal.
	acmicpc-live-archive.uva.es /nuevoportal/data/problem.php?p=3837 (220 words)

	[No title]
		Subject: Re: Stable marriages problem - looking for a proof Date: Thu, 5 Aug 1999 11:57:11 -0500 Newsgroups: sci.math Keywords: references On 5 Aug 1999, Remco Gerlich wrote: > For a lab session, I have to implement a program that finds a solution > for "the stable marriages problem".
		A marriage is unstable if there is a couple in the group that > isn't married, and that has each other higher on their preferences > list than their spouses.
		Dan Gusfield and Robert W. Irving, _The Stable Marriage Problem: Structures and Algorithms_, MIT Press, 1989.
	www.math.niu.edu /~rusin/known-math/99/stable_marriage (260 words)

	Stable Marriages - Wolfram Demonstrations Project
		A set of marriages is unstable if a man and woman within the set could improve their happiness by marrying each other rather than staying with their current partners.
		This Demonstration shows the set of stable marriages that results from having the men rank females on the basis of a distance measure from themselves to each female.
		A variant of the stable marriage algorithm is used to match applicants for medical residencies in the United States with hospitals using residents.
	demonstrations.wolfram.com /StableMarriages (274 words)

	Help Marriage Problem
		Fixing a marriage problem can work if both partners are willing to work on the problem in their marriage together.
		problem, for marriage statistics,, gay marriage,, arranged, marriage, texas, and marriage, for marriage sexless,.
		This book probes the stable marriage problem and its variants as a rich source of problems and ideas that illustrate both the design and analysis of efficient algorithms.
	www.savingyourmarriage.com /1/help-marriage-problem.html (735 words)

	Random stable matchings
		The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints.
		A stable matching is a pairing of adjacent vertices in a graph such that no unpaired vertices prefer each other to their partners under the matching.
		The problem of finding stable matchings is known as the stable marriage problem (on bipartite graphs) or as the stable room-mates problem (on the complete graph).
	www.iop.org /EJ/abstract/1742-5468/2005/10/P10008 (359 words)

	Glasgow University Theses Repository - Algorithmic aspects of stable matching problems
		The Stable Marriage problem (SM), the Hospitals/Residents problem (HR) and the Stable Roommates problem (SR) are three classical stable matching problems that were first studied by Gale and Shapley in 1962.
		Some of the problems that we consider are derived from new stable matching models, whilst others are obtained from existing stable matching models involving ties and incomplete lists, with additional natural restrictions on the problem instance.
		In the case of strong stability, for each of HRT and SRTI with a master list, we describe an algorithm that is faster than that for the general case.
	theses.gla.ac.uk /64 (760 words)

	UMBC CMSC771 Knowledge Representation and Reasoning
		Both problems give us a pair of disjoint sets and some additional data and then ask us to produce a bijection between the sets satisfying certain constraints.
		Nevertheless, the problems differ with respect to the nature of the given additional data and the constraints which any solution must satisfy.
		That means we must avoid creating any unmarried man-woman pair (M,w) where M prefers w to his wife and w prefers M to her husband.
	cgm.cs.mcgill.ca /~avis/courses/360/notes/stablemarriage.html (1473 words)

	[No title]
		The Stable Marriage Problem is related to several other problems in the field of combinatorics, which in general deals with finite objects, graphs, finite optimization problems, "counting", and other related topics.
		If there is a stable marriage between a man M and a woman W, we'll call M and W achievable partners.
		Then the results are optimal for the males in the sense that every male is married to his favorite acheivable partner, and similarly every woman is married to her least favorite achievable partner.
	www.math.cornell.edu /~numb3rs/samuelson/organs.html (1653 words)

	Marriage and Caste by Kay S. Hymowitz, City Journal Winter 2006
		Traditional marriage gives young people a map of life that takes them step by step from childhood to adolescence to college or other work training—which might well include postgraduate education—to the workplace, to marriage, and only then to childbearing.
		A marriage orientation also requires a young woman to consider the question of what man will become her husband and the father of her children as a major, if not the major, decision of her life.
		In other words, a marriage orientation demands that a woman keep her eye on the future, that she go through life with deliberation, and that she use self-discipline—especially when it comes to sex: bourgeois women still consider premature pregnancy a disaster.
	www.city-journal.org /html/16_1_marriage_gap.html (4491 words)

	DBLP: Shuichi Miyazaki
		Kazuo Iwama, Shuichi Miyazaki, Naoya Yamauchi: A 1.875: approximation algorithm for the stable marriage problem.
		Kazuo Iwama, Shuichi Miyazaki, Naoya Yamauchi: A (2-c(1/sqrt(N)))-Approximation Algorithm for the Stable* Marriage Problem.
		Kazuo Iwama, Shuichi Miyazaki, Kazuya Okamoto: A (2-c(log N/N))-Approximation Algorithm for the Stable Marriage Problem.
	www.informatik.uni-trier.de /~ley/db/indices/a-tree/m/Miyazaki:Shuichi.html (499 words)

	Capital Area Theory Seminar
		We are interested in the problem of reserving the least amount of the network capacity for protection, while guaranteeing fast restoration to all the supported connections, with the constraint that the maximum amount of protection one can put on a link is limited by the amount of existing traffic on that link.
		We show that the problem is NP-complete, and we present efficient approximation algorithms for the problem.
		A matching is unstable if there are a man and a woman which are not matched and would rather be together than with their current partner in the matching.
	www.cs.umd.edu /areas/Theory/CATS/catsf03.html (1660 words)

	Stable Marriage Problem
		This problem was first formulated by Gale and Shapley, two mathematicians/economists, back in 1962.
		The stable marriage problem interests me not only because of its useful applications (real world examples include college admission, dormitory arrangement, residents/hospitals assignment, and online dating, to name a few), but it has an incredibly beautiful structure behind it.
		In stable marriage, a classical theorem states that it is impossible that a group of cheating men can get better wives.
	www.cs.dartmouth.edu /~villars/research.html (468 words)

	[No title]
		Stable marriage with ties and unacceptable partners David Manlove, University of Glasgow, UK Abstract: An instance of the classical stable marriage problem involves n men and n women, and each person ranks all n members of the opposite sex in strict order of preference.
		A solution to the problem is a stable matching, i.e., a complete matching of the men and women such that no unmatched pair prefer each other to their partners in the matching.
		In this talk, I will summarise briefly the background to the stable marriage problem, and will describe some of the algorithmic results relating to the stable marriage problem in this extended setting, where a preference list no longer needs to be strictly ordered and complete.
	www.csc.liv.ac.uk /~leszek/lad99/dm.txt (161 words)

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