Generalize the conclusion to a subset of k pairs

Reference no: EM131333793

Given a stable matching of n men and n women,

(a) Is it possible to find three pairs such that if the matching among them is changed, each man will be matched to a woman whom he prefers, and each woman will be matched to a man whom she prefers?

(b) Generalize this conclusion to a subset of k pairs, for every 4 ≤ k ≤ n.

Reference no: EM131333793

Questions Cloud

Proximate and ultimate causes of the behavior : We all see animals in our day to day lives. Choose a behavior you saw exhibited by an animal. Explain your thoughts on the potential proximate and ultimate causes of the behavior.

Implement the first text-formatting design proposed : Implement the first text-formatting design proposed. Try to avoid the need for shifting word fragments after the current line is printed.

Prove the given condition : Prove that if the result of the men's courtship algorithm yields the same result as the women's courtship algorithm, then this resulting matching is the unique stable matching.

Description of probability and nonprobability sampling : Post a description of the types of probability and non-probability sampling you selected. Then describe two strengths and two weaknesses of each type of sampling. Finally, identify two ethical considerations that may factor into selecting a sampli..

Generalize the conclusion to a subset of k pairs : Is it possible to find three pairs such that if the matching among them is changed, each man will be matched to a woman whom he prefers, and each woman will be matched to a man whom she prefers?

Implement this hash search method : If items are retrieved from a hash table with unequal frequencies a gradual speed-up in retrieval can be obtained by shifting each item as it is retrieved one position closer to its original hash position by performing an exchange. Implement this ..

Is there necessarily a stable matching : Is there necessarily a stable matching under which Julius is matched to Messalina? Either prove this statement or provide a counter example.

Explored importance of conceptualizing and defining variable : In previous weeks of the course, you explored the importance of conceptualizing and defining variables. Those tasks set the guidelines for research and have many important consequences for the results

Prove that the mens courtship algorithm terminates : Prove that the men's courtship algorithm terminates after at most (n - 1)2 + 1 stages.- Find preference relations under which the algorithm terminates after precisely (n - 1)2 + 1 stages.

User Account

All Pages