Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

Write the deferred acceptance algorithm in pseudocode.

$(P_{a}, w_{a})$ is pair of women and their accepted proposals.

And return is $(P_{a}, w_{a})$ for all $a \in \{1, 2, . . ., n\}$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1:

We will use ‘match’ algorithm.

Procedure match

$(m_{1}, m_{2}, \dots, m_{n}, w_{1}, w_{2}, \dots ., w_{n} with preference lists M_{1}, M_{2}, \dots M_{n}, W_{1}, W_{2}, \dots W_{n}, respectively)$

Here $p_{i}$ is the proposal list of women $w_{i}$ .

Every man proposes to their preferred women and the women reject the proposal of all the men that are not their preferred man from the entire proposal. When the men will propose to the first women in their remaining preference list and the women will reject all the proposals of their no preferred men.

This will repeat until all women have exactly one remaining proposal.

Step 2:

For i : = 1 to n ,

$P_{i : =} ϕ$

While there exists a $P_{i}$ with $i \in \{1, 2, . . ., n\}$ such that $P_{i : =} ϕ$

For j : = 1 to n

$P_{M_{i} (1)} : = P_{M_{i} (1)} \cup \{M_{j}\}$

For k : = 1 to n

best = $p_{k} (1)$

Step 3

For all $p \in P_{k}$ do if p is preferred over best in $W_{k}$ then,

$M_{b e s t} : = M_{b e s t} - w_{k}$

Else

$M_{p} : = M_{p} - \{w_{k}\}$

Hence, $(P_{a}, w_{a})$ is pair of women and their accepted proposals.

And return is $(P_{a}, w_{a})$ for all $a \in \{1, 2, . . ., n\}$

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Discrete Mathematics and its Applications

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Write the deferred acceptance algorithm in pseudocode.

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