Stable matching | Combinatorics | Game theory | Mathematical problems | Cooperative games
In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of the other set. A matching is not stable if: 1. * There is an element A of the first matched set which prefers some given element B of the second matched set over the element to which A is already matched, and 2. * B also prefers A over the element to which B is already matched. In other words, a matching is stable when there does not exist any pair (A, B) which both prefer each other to their current partner under the matching. The stable marriage problem has been stated as follows: Given n men and n women, where each person has ranked all members of the opposite sex in order of preference, marry the men and women together such that there are no two people of opposite sex who would both rather have each other than their current partners. When there are no such pairs of people, the set of marriages is deemed stable. The existence of two classes that need to be paired with each other (heterosexual men and women in this example) distinguishes this problem from the stable roommates problem. (Wikipedia).
Bad intro for the Stable Marriage Problem
So, not all clips make the cut. This one didn't. Here's the main video: https://youtu.be/A7xRZQAQU8s Here's the AAA chapter: https://leios.gitbooks.io/algorithm-archive/content/chapters/computational_mathematics/decision_problems/stable_marriage/stable_marriage.html The music came from J
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Arguments When There Is Too Little Sex
There's a special kind of argument that can arise in a couple when, for a range of reasons, there hasn't been enough sex. Unfortunately, couples tend to feel too ashamed to mention what the argument is really about - and so squabble about essentially unrelated things. Even worse, the fact
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What are the Alternatives to Marriage?
Marriage brings with it a lot of problems; are there some alternatives? If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/5Wo4j5 Join our exclusive mailing list: http://bit.ly/2e0TQNJ Or visit us in person at our London HQ https://goo.gl/Ajlatn FURTHER
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The Stable Marriage Problem (Gale-Shapley Algorithm)
This one took me a while because the algorithm is actually a bit tricky to implement correctly. That said, it was super fun. I hope you guys enjoy implementing it! Here's the AAA chapter: https://www.algorithm-archive.org/chapters/decision_problems/stable_marriage/stable_marriage.html If
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From many points of view, marriage is a costly hassle that makes no sense. Why, then, might there still be good reasons to get married? If you like our films, take a look at our shop (we ship worldwide): http://bit.ly/2bfBplr Our website has classes, articles and products to help you
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Is 'separation marriage' key to a healthy relationship? – BBC News
In Japan, there has been a rise in 'separation marriages' or 'weekend marriages'. The unusual arrangement sees couples living separately in their own homes – prioritising their own lifestyle and needs – whether that's their job, social life, hobbies or childcare. But does it work? And is
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The rules for how to doom a relationship are relatively easy to follow. Here are a selection that are guaranteed to blow up love. Please subscribe here: http://tinyurl.com/o28mut7 If you like our films take a look at our shop (we ship worldwide): http://www.theschooloflife.com/shop/all/ B
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Why You Will Marry the Wrong Person
You'll try not to of course - but you will, unwittingly. At least there is comfort in knowing you're not alone. For gifts and more from The School of Life, visit our online shop: https://goo.gl/FEJWIK FURTHER READING “Anyone we might marry could, of course, be a little bit wrong f
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MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
A Solution to the Stable Marriage Problem: Emily Riehl Public Lecture
In her Perimeter Public Lecture webcast on May 12, 2021, mathematician Emily Riehl will examine the fascinating mathematics providing a solution to the stable marriage problem, including the sexist implications underlying it and some real-world applications. Riehl, an associate professor o
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Stable Marriage Problem (the math bit)
Continues from: http://youtu.be/Qcv1IqHWAzg Featuring Dr Emily Riehl. Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Google Plus: http://bit.ly/numberGplus Tumblr: http://numberphile.tum
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Stuff From The Future - The Future of Relationships
Technology isn't just changing the way people encounter new information -- it's also changing the way people encounter each other. Tune in as Cristen explains how technology will affect relationships, families and children in the future. http://howstuffworks.com http://itunes.apple.com
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Mother's Day Special: Variation of the Stable Marriage Problem
In this Holiday Special, Tori describes the famous Stable Matching (or Marriage) Problem, but with a Mother's Day theme. Happy Mother's Day to all moms watching our math videos! Here's the link to the blog post detailing the mathematics: http://centerofmathematics.blogspot.com/2015/05/mot
From playlist Center of Math BLOG: Holiday Mathematics
離散数学入門#12: マッチング(3):安定結婚問題とGale–Shapleyアルゴリズム,臨床研修マッチングへの応用
早稲田大学の全学部の3〜4年生を対象とする全学オープン科目「離散数学入門」(担当教員:早水 桃子)の授業動画です.文理を問わず,誰でもグラフ理論やグラフアルゴリズムの初歩を学ぶことができます.グラフ理論の定理やグラフに関するアルゴリズムを正しく理解して,現実の諸問題を解決するための応用力を身につけましょう. --------------------------------------------------------------------------------------- 最大マッチングが全体の利益を最大化するマッチングであるのに対して,安定マッチングは個人の選好を
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Why Queer Relationship Dynamics are Harder: The Stable Marriage Problem #SoME2
Sources Dr. Emily Riehl solving the Stable Marriage Problem on Numberphile: https://www.youtube.com/watch?v=LtTV6rIxhdo Gale and Shapley's original paper: https://www.jstor.org/stable/2312726 Irving's 1984/5 solution to the Stable Roommates Problem: https://www.sciencedirect.com/science/ar
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2.11.5 Optimal Stable Matching: Video
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
The Stable Marriage Problem (2012 Nobel Prize Economics)
How can you match N men and N women for marriage, so each person gets their highest preference? This is the stable marriage problem, and it has many applications, like how to match doctors into residency programs. The Gale-Shapley algorithm always finds a solution. This video illustrates t
From playlist Game Theory
There is no Nobel Prize in mathematics. Find out how you can still earn yourself one if you are a mathematician. Featuring Gale and Shapley's stable marriage theorem and and the debunking of a popular sex statistics myth. In my life before YouTube I together with my colleague and friend
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Stable Marriage Problem - Numberphile
Discuss on Reddit: http://redd.it/2fgu97 More links & stuff in full description below ↓↓↓ Featuring Dr Emily Riehl. Continues with the more mathematical bit at: http://youtu.be/LtTV6rIxhdo The Gale/Shapley paper: http://bit.ly/StableMarriage Animation and artwork by Pete McPartlan. (But t
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Which Long-term Relationships Will Survive and Which Won't
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