1. Lecture 5
CSE 331
Sep 5, 2014

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. Schedules and Deadlines

5. Schedules and Deadlines

7. Sign-up for mini projects
me your group (=6) composition + your chosen algorithm

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

9. Remember to read HW policies

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

11. On matchings
Mal
Wash
Simon
Inara
Zoe
Kaylee

12. A valid matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

13. Not a matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

14. Perfect Matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

15. Preferences
Mal
Wash
Simon
Inara
Zoe
Kaylee

16. Instability
Mal
Wash
Simon
Inara
Zoe
Kaylee

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

18. Two stable marriages

19. 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 polyandry/gamy in M X W)
Perfect Matching (everyone gets married) m w m’ w’
Instablity
Stable matching = perfect matching+ no instablity

20. Questions/Comments?

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

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

23. Discuss: Naïve algorithm!

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

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

26. Moral of the story…
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27. Questions/Comments?

28. 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

29. Preferences
Mal
Wash
Simon
Inara
Zoe
Kaylee

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