Question: Consider an instance of the stable matching problem with n men and n women. Let X and Y be some two stable matchings for this

Consider an instance of the stable matching problem with n men and n women. Let X and Y be some two stable matchings for this instance. We now construct a new pairing Z as follows. For each man m, if X pairs him with a woman w^m_x and Y pairs him with a woman w^m_ythen in Z the man is paired with the woman he prefers most among w^m_x and w^m_y. Note that w m x and w m y could be the same woman.

A) Prove or disprove that Z is a stable matching.

B) Now consider a pairing Z' in which a man m is paired with the woman he prefers the least among w^m_x and w^m_y. Prove or disprove that Z' is a stable matching.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The question is complete Lets proceed with the solution A Prove or Disprove that Z is a Stable Matching To assess whether Z is a stable matching we ne... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

4. (20 pt) Let m1,m2 be two of the men and w1,w2 be two of the women in an instance of the Stable Matching Problem with n men and n women. Assume m1,m2,w1,w2 's preference lists are: m1 's...

Let m, m be two of the men and w, w be two of the women in an instance of the Stable Matching Problem with n men and n women. Assume m, M, W, W2's preference lists are: m's preference: W > W>.. m's...

(20 pt) Let m1,m2 be two of the men and w1,w2 be two of the women in an instance of the Stable Matching Problem with n men and n women. Assume m1,m2,w1,w2 's preference lists are:...

Consider an instance of the stable matching problem with 4 men and 4 women. Provide their preference lists as you want (show them using two tables as in the slides). Then provide an assignment that...

( 1 0 points ) True or False? For each of the statements below, determine whether it is True or False. Then, briefly explain your answers or provide counterexamples. Incorrect answers or unanswered...

2 Pairing U p Prove that for every even n 2 , there exists an instance of the stable matching problem with n jobs and n candidates such that the instance has at least 2 n 2 distinct stable matchings.

(Number of Stable Matchings) The analysis of the Gale-Shapley algorithm establishes that every instance of the stable matching problem admits at least one stable matching. Here we consider how many...

The county finance department in Exercise 7.90 also wants information about renewals of disabled parking placards. Suppose that in a sample of 350 transactions for disabled parking placards, it was...

Once inside the host cell, phage DNA A) is replicated. B) is transcribed. C) may get degraded by bacterial nucleases. D) may integrate into the host chromosome. E) All of the choices are correct.

A financial analyst is estimating the effect on the cost of capital for a company of a decrease in the marginal tax rate. The company is financed with debt and common equity. A decrease in the firm's...

Questions Q1. Write a Python program to retrieve the first and last colors from the following list: color_list = ["red", "green", "white", "blue", "black") Q2. Given the following dictionary,...