Matching Theory, Marriage Problem
Consider an arbitrary marriage problem in which agents on one side, say women, have the same preference ordering of the men. Find a stable matching. Is it a unique stable matching? If so, prove its uniqueness. Otherwise, provide a counter example.
Homework Answers
Write a concurrent program to solve stable marriage problem using Akka with Java. Be sure to...
Write a concurrent program to solve stable marriage problem using Akka with Java. Be sure to explain your solution strategy Given n men and n women and a preference order of marriage from each one of them, how to marry these 2n bachelors such that their marriages are stable. A marriage is stable when both partners in a couple cannot find anyone else (higher in their priority list) available for marriage. In other words, a marriage is stable when every...
1 Intro The Stable Matching problem is solved with the Gale-Shapley algorithm. Here is the description...
1 Intro The Stable Matching problem is solved with the Gale-Shapley algorithm. Here is the description of the Gale-Shapley algorithm from the Kleinberg text. It talks about a matching between equal numbers of men and women. 1 Initially all me M and wE W are free 2 While there is a man m who is free and hasn't proposed to every woman Choose such a man m Let w be the highest-ranked woman in m's preference list to whom m...
Question 1: Consider the following Monty Hall problem. Suppose you are on a game show, and...
Question 1: Consider the following Monty Hall problem. Suppose you are on a game show, and you are given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what is behind the doors, opens another door, say #3, which has a goat. Here we assume that the host cannot open the door to expose the car and when he can open either of...
Problem 2 a) In how many ways can 6 women and 5 men line up so...
Problem 2 a) In how many ways can 6 women and 5 men line up so that no two men are next to one another? b) In how many ways can 7 different pairs of twins line up so that twins must be next to one another? c) In how many ways can 7 women and 10 men sit at a circular table so that no two women are sitting side by side? d) How many strings of length 5...
As you have read in the document describing the treatment/status of women in Taliban enclaves, this...
As you have read in the document describing the treatment/status of women in Taliban enclaves, this treatment/status is significantly different from the general treatment/status of women in the United States. Consider the following two characterizations of this difference in treatment/status: [a] Men and women are moral equals. As moral equals women are entitled to the same consideration of their interests, wants, and individual happiness that is given to men. Societies, communities, groups who think and act otherwise [groups such as...
4. There are 4 boys (A, B, C, D) and 4 girls (a, b, c, d)...
4. There are 4 boys (A, B, C, D) and 4 girls (a, b, c, d) who want to date. Each boy has a preference list, and so does each girl. A pair of a boy and a girl is called unstable if the boy has another girl he likes better, and so does the girl. For example, if the preference list of A is b > c > a > d and that of a is B > A...
Problem 1. (The golden mean] In this problem you will find the exact value of the...
Problem 1. (The golden mean] In this problem you will find the exact value of the number 7, often called the golden mean or the golden ratio (sometimes this terminology is used for 7-1). The golden mean is defined by the following expression: 7= 1+- 1+ - 1 1+ 1+... (a) Consider the iteration Xn+1 = f(xn), where x1 = 1, and 1 f(x) = 1+2 1 1+: Recall the following result. Theorem. (i) If the function g : [a,...
The Problem: Depress the equation r6r +100 1. Decomposing a cube: Consider a cube with side length (a) Suppose we...
The Problem: Depress the equation r6r +100 1. Decomposing a cube: Consider a cube with side length (a) Suppose we break the side of the cube at an arbitrary point ryb. This cut triggers the decomposition of the cube into the 8 pieces you have with your manipulative. You will have a cube with side length y and a cube with side length b. Identify the other 6 solids in terms of their dimensions using y and b so that...
this is related to machine learning problem QuestioIl J. (10 MARKS Alberta Hospital occasionally has electrical...
this is related to machine learning problem
QuestioIl J. (10 MARKS Alberta Hospital occasionally has electrical problems. It can take some time to find the problem, though it is always found in no more than 10 hours. The amount of time is variable; for example, one time it might take 0.3 hours, and another time it might take 5.7 hours. The time in hours) necessary to find and fix an electrical problem at Alberta Hospital is a random variable, say...
How have our ideas on "Marriage" and "Family" changed in the last 100 years? Images used...
How have our ideas on "Marriage" and "Family" changed in the last 100 years? Images used in marketing and advertising can speak volumes about the norms, values, and ideals of a particular generation. Here is an example: Look at how we market an image of what is “healthy”. If you look at any tabloid magazine cover while you are waiting to check out with your groceries (if you normally don't look, next time consciously do so!), you will find that,...
Write a concurrent program to solve stable marriage problem using Akka with Java. Be sure to explain your solution strategy Given n men and n women and a preference order of marriage from each one of them, how to marry these 2n bachelors such that their marriages are stable. A marriage is stable when both partners in a couple cannot find anyone else (higher in their priority list) available for marriage. In other words, a marriage is stable when every...
1 Intro The Stable Matching problem is solved with the Gale-Shapley algorithm. Here is the description of the Gale-Shapley algorithm from the Kleinberg text. It talks about a matching between equal numbers of men and women. 1 Initially all me M and wE W are free 2 While there is a man m who is free and hasn't proposed to every woman Choose such a man m Let w be the highest-ranked woman in m's preference list to whom m...
4. There are 4 boys (A, B, C, D) and 4 girls (a, b, c, d) who want to date. Each boy has a preference list, and so does each girl. A pair of a boy and a girl is called unstable if the boy has another girl he likes better, and so does the girl. For example, if the preference list of A is b > c > a > d and that of a is B > A...
Problem 1. (The golden mean] In this problem you will find the exact value of the number 7, often called the golden mean or the golden ratio (sometimes this terminology is used for 7-1). The golden mean is defined by the following expression: 7= 1+- 1+ - 1 1+ 1+... (a) Consider the iteration Xn+1 = f(xn), where x1 = 1, and 1 f(x) = 1+2 1 1+: Recall the following result. Theorem. (i) If the function g : [a,...
The Problem: Depress the equation r6r +100 1. Decomposing a cube: Consider a cube with side length (a) Suppose we break the side of the cube at an arbitrary point ryb. This cut triggers the decomposition of the cube into the 8 pieces you have with your manipulative. You will have a cube with side length y and a cube with side length b. Identify the other 6 solids in terms of their dimensions using y and b so that...
this is related to machine learning problem
QuestioIl J. (10 MARKS Alberta Hospital occasionally has electrical problems. It can take some time to find the problem, though it is always found in no more than 10 hours. The amount of time is variable; for example, one time it might take 0.3 hours, and another time it might take 5.7 hours. The time in hours) necessary to find and fix an electrical problem at Alberta Hospital is a random variable, say...
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