1. Lecture 4
CSE 331
Sep 4, 2013

2. Office Hours Beth: Wed + Fri 11:00-11:50am Jerry: Mon 11:00-11:50am
Davis
302
Jerry: Mon 11:00-11:50am
+ Th 10:00-10:50am
Atri: Mon, Wed 2-2:50pm

3. Submit the form
I’ll need confirmation in writing. No graded material will be handed back till
I get this signed form from you!

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

5. National Resident Matching

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

7. The situation can be unstable!

8. What happens in real life
Preferences
Information
Preferences

9. NRMP plays matchmaker

10. Questions/Comments?

11. 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

12. Simplicity is good

13. 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?

14. Questions/Comments?

15. Discuss: Naïve algorithm!

16. 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

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

18. Moral of the story…
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