suppose in an instance of the stable matching problem there are n men and n +...
suppose in an instance of the stable matching problem there are n men and n + m women, where m ≥ 0. Which of the following conclusions can be inferred?
Homework Answers
--> The number of men is n and number of women is n+m.
(i) there will be some woman left out.
(ii) men will have best partner they can have in any stable matching.
Add Answer to:
suppose in an instance of the stable matching problem there are
n men and n +...
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.
9. Suppose we have a solution to the n-Queens problem instance in which n 4. Can...
9. Suppose we have a solution to the n-Queens problem instance in which n 4. Can we extend this solution to find a solution to the problem instance in which n 5? Can we then use the solutions for n 4 and n 5 to construct a solution to the instance in which n 6 and continue this dynamic programming approach to find a solution to any instance in which n 4? Justify your answer.
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...
1.2 Find a stable marriage matching for the instance defined by the following ranking matrix. Break...
1.2 Find a stable marriage matching for the instance defined by the following ranking matrix. Break a tie using the alphabetic order. Draw a matrix after each iteration, and describe what happens in the iteration, using the format of Figure 10.12. When the process is over, write the matching a B y S A 1,3 1,4 2,2 4,1 B 2,3 4,1 1,4 2,2 C 3,2 3,4 3,3 3,1 D 4,3 2,2 4,1 1,4 AN
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...
Suppose you are given an instance of the fractional knapsack problem in which all the items...
Suppose you are given an instance of the fractional knapsack problem in which all the items have the same weight. Show that you can solve the fractional knapsack problem in this case in O(n) time.
The 3-Dimensional Matching (3DM) decision problem takes as input three sets \(A, B\), and \(C\), each...
The 3-Dimensional Matching (3DM) decision problem takes as input three sets \(A, B\), and \(C\), each having size \(n\), along with a set \(S\) of triples of the form \((a, b, c)\) where \(a \in A, b \in B\), and \(c \in C\). We assume that \(|S|=m \geq n\). The problem is to decide if there exists a \(3 \mathrm{DM}\) matching, i.e. a subset of \(n\) triples from \(S\) for which each member of \(A \cup B \cup C\) belongs...
Problem 3 A group of n couples composed of n men and n women enter a...
Problem 3 A group of n couples composed of n men and n women enter a restaurant and sit randomly at n tables, two on each. i. Find the expected number of tables occupied by two people of different gender. ii. Find the expected number of tables occupied by couples. iii. If the n women enter the restuarant first and each sits at a separate table and then the men enter and sit randomly at the n tables. Find the...
Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a...
Suppose that, in a divide-and-conquer algorithm, we always
divide an instance of size n of a problem into 5 sub-instances of
size n/3, and the dividing and combining steps take a time
in Θ(n n). Write a recurrence equation for the running time T
(n) , and solve the
equation for T (n)
2. Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a problem into 5 sub-instances of size n/3, and the dividing...
3. Suppose you are asked to draw a random sample of men and women in order...
3. Suppose you are asked to draw a random sample of men and women in order to measure their "emotional IQ'. The emotional IQ scale that you administer has a minimum of 0 and a maximum of 100, with higher scores indicating higher emotional intelligence. You sample 25 men and 25 women. The mean for men is 70 with a standard deviation of 10, and the mean for women is 82 with a standard deviation of 15. Using this information,...
9. Suppose we have a solution to the n-Queens problem instance in which n 4. Can we extend this solution to find a solution to the problem instance in which n 5? Can we then use the solutions for n 4 and n 5 to construct a solution to the instance in which n 6 and continue this dynamic programming approach to find a solution to any instance in which n 4? Justify your answer.
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...
1.2 Find a stable marriage matching for the instance defined by the following ranking matrix. Break a tie using the alphabetic order. Draw a matrix after each iteration, and describe what happens in the iteration, using the format of Figure 10.12. When the process is over, write the matching a B y S A 1,3 1,4 2,2 4,1 B 2,3 4,1 1,4 2,2 C 3,2 3,4 3,3 3,1 D 4,3 2,2 4,1 1,4 AN
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...
Problem 3 A group of n couples composed of n men and n women enter a restaurant and sit randomly at n tables, two on each. i. Find the expected number of tables occupied by two people of different gender. ii. Find the expected number of tables occupied by couples. iii. If the n women enter the restuarant first and each sits at a separate table and then the men enter and sit randomly at the n tables. Find the...
Suppose that, in a divide-and-conquer algorithm, we always
divide an instance of size n of a problem into 5 sub-instances of
size n/3, and the dividing and combining steps take a time
in Θ(n n). Write a recurrence equation for the running time T
(n) , and solve the
equation for T (n)
2. Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a problem into 5 sub-instances of size n/3, and the dividing...
3. Suppose you are asked to draw a random sample of men and women in order to measure their "emotional IQ'. The emotional IQ scale that you administer has a minimum of 0 and a maximum of 100, with higher scores indicating higher emotional intelligence. You sample 25 men and 25 women. The mean for men is 70 with a standard deviation of 10, and the mean for women is 82 with a standard deviation of 15. Using this information,...
Most questions answered within 3 hours.
-
In this exercise, we will be refactoring a working program. Code
refactoring is a process to...
asked 1 hour ago -
3
researchers at Cambrige looked at 5,000 firms in Englans and found
that, in terms of...
asked 50 minutes ago -
why it is important and how it integrates within ERP? And what
the core challenges of...
asked 2 hours ago -
A strawberry farmer determines that the average weight of
individual strawberries produced by plants in his...
asked 3 hours ago -
Chargaff's results yielded a molar ratio of 0.400 for A to G in
avian tubercle bacillus...
asked 5 hours ago -
Which of the following binds ATP/ADP?
a. microfilaments
b. microtubules
c. intermediate filaments
d. microfilaments and...
asked 5 hours ago -
Assume that the situation can be expressed as a linear cost
function. Find the cost function....
asked 7 hours ago -
(Sort ArrayList) Write the following method that sorts an
ArrayList: public static > void sort(ArrayList list)...
asked 7 hours ago -
2) A 9 volt battery is connected to a parallel plate capacitor
with an initial capacitance...
asked 7 hours ago -
Prince Equipment has to decide whether to obtain $1,000,000 of
financing by: (1) selling common stock...
asked 8 hours ago -
The terms electrical and electronic have similar but
different meanings which of the following statement is...
asked 8 hours ago -
You wish to test the claim that the mean GPA of night students
is than 2.5...
asked 8 hours ago