1. Lecture 3
CSE 331
Sep 1, 2017

2. Enroll on Piazza

3. Read the syllabus CAREFULLY!
No graded material will be handed back till you submit a signed form!

4. Autolab FAQ

5. TA office hours
Finalized by Monday

6. Two comments on Programming
Programming is worth about 12% of your final grade
Algorithm design/proofs are worth about 82% of your final grade
Invest your time wisely
C++, Java, Python from HW 1
331 is not the place to learn a new language!

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

8. National Resident Matching

9. (Screen) Docs are coming to BUF
Buffalo General
Bailey (Grey’s Anatomy)
Millard Filmore (Gates Circle)
JD (Scrubs)
Millard Filmore (Suburban)

10. What can go wrong?

11. The situation is unstable!

12. What happens in real life
Preferences
Information
Preferences

13. NRMP plays matchmaker

14. Stable Matching Problem
David Gale
Lloyd Shapley

15. Questions/Comments?

16. 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

17. Simplicity is good

18. 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?

19. Questions/Comments?

20. Non-feminist reformulation
n men
Each with a preference list
n women
Match/marry them in a “stable” way

21. On matchings
Mal
Wash
Simon
Inara
Zoe
Kaylee

22. A valid matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

23. Not a matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

24. Perfect Matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

25. Preferences
Mal
Wash
Simon
Inara
Zoe
Kaylee

26. Instability
Mal
Wash
Simon
Inara
Zoe
Kaylee

27. Questions/Comments?

28. Discuss: Naïve algorithm!

29. 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

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

31. Moral of the story…
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