1. Lecture 5
CSE 331
Sep 10, 2010

2. HW 1
Posted on course webpage
READ THE INSTRUCTIONS CAREFULLY

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

4. Only 71 signed forms
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I get this signed form from you!

5. One new blog post slot open
Sep 15 has one free slot now

6. On matchings
Mal
Wash
Simon
Inara
Zoe
Kaylee

7. A valid matching

8. Not a matching

9. Perfect Matching

10. Preferences

11. Instability

12. Questions/Comments?

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. First algorithm?
Try to match up one man and women who prefer each other most
n! perfect matchings
Go through all perfect matchings S
If S is stable then stop else move to the next matching

15. Verify if perfect matching is stable
Go through all pairs (m,w)
n^2 pairs
Check if m and w *both* prefer each other to their current matchings
O(n) time
If so matching is unstable
O(n^3) time

16. Today’s lecture Couple of examples
Gale-Shapley algorithm for Stable Marriage problem

17. 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