1. Lecture 5
CSE 331
Sep 6, 2013

2. Submit the form
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
me your group (=6) composition + your chosen algorithm

4. Homeworks HW 1 posted online: see piazza
Pickup graded HW 0 starting Monday

5. Remember to read the HW policies

6. Separate Proof idea/proof details
Proof details with no proof idea will get you a zero for the entire problem

7. Talks by Ed Lazowska

8. On matchings
Mal
Wash
Simon
Inara
Zoe
Kaylee

9. A valid matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

10. Not a matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

11. Perfect Matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

12. Preferences
Mal
Wash
Simon
Inara
Zoe
Kaylee

13. Instability
Mal
Wash
Simon
Inara
Zoe
Kaylee

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

15. Two stable marriages

16. 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

17. Questions/Comments?

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

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

20. Discuss: Naïve algorithm!

21. 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

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

23. Moral of the story…
>

24. Questions/Comments?

25. 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

26. Preferences
Mal
Wash
Simon
Inara
Zoe
Kaylee

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