1. Lecture 4
CSE 331
Sep 3, 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. More clarification on sources

4. Office Hours Frank: Tue + Th 1:00-1:50pm Zulkar: Wed 4:00-4:50pm
Davis
302
Zulkar: Wed 4:00-4:50pm
+ Th 2:00-2:50pm
Atri: Mon 2-2:50pm
Wed 3-3:50pm

5. Main Steps in Algorithm Design
Problem Statement
Real world problem
Problem Definition
Precise mathematical def
Algorithm
“Implementation”
Data Structures
Analysis
Correctness/Run time

6. National Resident Matching

7. (Screen) Docs are coming to BUF
Buffalo General
Hawkeye (M*A*S*H)
Millard Filmore (Gates Circle)
JD (Scrubs)
Millard Filmore (Suburban)

8. The situation can be unstable!

9. What happens in real life
Preferences
Information
Preferences

10. NRMP plays matchmaker

11. Questions/Comments?

12. Matching Employers & Applicants
Input: Set of employers (E)
Set of applicants (A)
Preferences
Output: An assignment of applicants to employers that is “stable”
For every x in A and y in E such that x is not assigned to y, either
(i) y prefers every accepted applicant to x; or
(ii) x prefers her employer to y

13. Simplicity is good

14. Questions to think about
1) How do we specify preferences?
Preference lists
2) Ratio of applicant vs employers
1:1
3) Formally what is an assignment?
(perfect) matching
4) Can an employer get assigned > 1 applicant? NO
5) Can an applicant have > 1 job?
6) How many employer/applicants in an applicants/employers preferences?
All of them
7) Can an employer have 0 assigned applicants? NO
8) Can an applicant have 0 jobs?

15. Questions/Comments?

16. Discuss: Naïve algorithm!

17. 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

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

19. Moral of the story…
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