1. Lecture 6
CSE 331
Sep 13, 2010

2. New tougher deadline If you do not form a group by Sep 14
You will get a ZERO on group leader scribe

3. Return signed forms
I’ll need confirmation in writing. No graded material will be handed back till
I get this signed form from you!

4. HW 0 solutions posted
Use them as model solutions for your future HWs

5. The Brangelina show…

6. Not a stable marriage

7. Even though BBT and JA are not very happy
A stable marriage
Even though BBT and JA are not very happy

8. The naïve algorithm Go through all possible perfect matchings S
n! matchings
If S is a stable matching
then Stop
Else move to the next perfect matching

9. Gale-Shapley Algorithm
David Gale
Lloyd Shapley
O(n3) algorithm

10. Moral of the story…
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11. Gale-Shapley Algorithm
Intially all men and women are free
While there exists a free woman who can propose
Let w be such a woman and m be the best man she has not proposed to
w proposes to m
If m is free
(m,w) get engaged
Else (m,w’) are engaged
If m prefers w’ to w
w remains free
Else
(m,w) get engaged and w’ is free
Output the engaged pairs as the final output

12. Preferences

13. GS algorithm: Firefly Edition1 2 3 4 5 6 1