1. Lecture 5
CSE 331
Sep 7, 2012

2. Not all signed forms turned in
I’ll need confirmation in writing. No graded material will be handed back till
I get this signed form from you!

3. Sign-up for mini projects
Send in THREE choices for dates

4. Homeworks HW 1 posted online: see blog/piazza
Pickup graded HW 0 in TA OHs

5. On matchings
Mal
Wash
Simon
Inara
Zoe
Kaylee

6. A valid matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

7. Not a matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

8. Perfect Matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

9. Preferences
Mal
Wash
Simon
Inara
Zoe
Kaylee

10. Instability
Mal
Wash
Simon
Inara
Zoe
Kaylee

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

12. Two stable marriages

13. Stable Marriage problem
Input: M and W with preferences
Output: Stable Matching
Set of men M and women W
Preferences (ranking of potential spouses)
Matching (no polygamy in M X W)
Perfect Matching (everyone gets married) m w m’ w’
Instablity
Stable matching = perfect matching+ no instablity

14. Questions/Comments?

15. Two Questions Does a stable marriage always exist?
If one exists, how quickly can we
compute one?

16. Today’s lecture Naïve algorithm
Gale-Shapley algorithm for Stable Marriage problem

17. Discuss: Naïve algorithm!

18. 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

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

20. Moral of the story…
>

21. Questions/Comments?

22. 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

23. Preferences
Mal
Wash
Simon
Inara
Zoe
Kaylee

24. GS algorithm: Firefly Edition
Mal
Inara 1 2 3 4 5 6
Wash
Zoe 1
Simon
Kaylee