The deferred acceptance algorithm can be used to construct an assignment of men and women. In this algorithm, members of one gender are the suitors and members of the other gender the suitees. The algorithm uses a series of rounds; in each round every suitor whose proposal was rejected in the previous round proposes to his or her highest ranking suitee who has not already rejected a proposal from this suitor. The suitees reject all the proposals except that from the suitor that this suitee ranks highest among all the suitors who have proposed in this round or previous rounds. The proposal of this highest ranking suitor remains pending and is rejected in a later round if a more appealing suitor proposes in that round. The series of rounds ends when every suitor has exactly one pending proposal. All pending proposals are then accepted. a) Write the deferred acceptance algorithm in pseudocode. b) Show that the deferred acceptance algorithm terminates. c) Show that the deferred acceptance always terminates with a stable assignment

The deferred acceptance algorithm can be used to construct an assignment of men and women. In this algorithm, members of one gender are the suitors and members of the other gender the suitees. The algorithm uses a series of rounds; in each round every suitor whose proposal was rejected in the previous round proposes to his or her highest ranking suitee who has not already rejected a proposal from this suitor. The suitees reject all the proposals except that from the suitor that this suitee ranks highest among all the suitors who have proposed in this round or previous rounds. The proposal of this highest ranking suitor remains pending and is rejected in a later round if a more appealing suitor proposes in that round. The series of rounds ends when every suitor has exactly one pending proposal. All pending proposals are then accepted. a) Write the deferred acceptance algorithm in pseudocode. b) Show that the deferred acceptance algorithm terminates. c) Show that the deferred acceptance always terminates with a stable assignment

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter13: Decision Making Under Uncertainty

Section13.4: Decision Trees

Problem 9P

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A men and women's assignment can be created using the postponed acceptance procedure. Members of one gender act as suitors in this algorithm, while members of the opposite gender act as suitees. Every suitor whose proposal was rejected in the previous round makes a proposal to his or her highest-ranking suitee who has not yet rejected this suitor in the algorithm's sequence of rounds. Except for the suitor who ranks highest among all the suitors who have proposed in this round or prior rounds, the suitees reject all the proposals. This highest ranking suitor's proposal is still pending and will be rejected if a more alluring suitor makes a proposal in a later round. The series of rounds ends when every suitor has exactly one pending proposal. All pending proposals are then accepted.a) Write the deferred acceptance algorithm in pseudocode.b) Show that the deferred acceptance algorithm terminates.c) Show that the deferred acceptance always terminates with a stable assignment
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