1. Lecture 5
CSE 331
Sep 9, 2011

2. Homework 1 has been posted
READ THE INSTRUCTIONS VERY CAREFULLY
Posted online (link on the blog)
Grading rubric will be posted by Tuesday next week

3. Graded HW 0
Pick up in recitations or TA office hours next week

4. 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!

5. A puzzle (if you’re bored)
For any n, what is the maximum number of
stable matchings (for the same problem instance)?
Prove as tight upper and lower bounds as you can.

6. If you’re free this weekend

7. Questions/Comments?

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

9. 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

10. Difference from the book
In the book’s description, the men do the proposing

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

12. Once a man gets engaged, he remains engaged (to “better” women)
Observation 1
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
Once a man gets engaged, he remains engaged (to “better” women)
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

13. If w proposes to m after m’, then she prefers m’ to m
Observation 2
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
If w proposes to m after m’, then she prefers m’ to m
(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

14. Today’s lecture At most n2 iterations of the while loop
GS algorithms always outputs a stable marriage