1. Lecture 3
CSE 331
Sep 2, 2016

2. Read the syllabus CAREFULLY!
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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. What can go wrong?

8. The situation is unstable!

9. What happens in real life
Preferences
Information
Preferences

10. NRMP plays matchmaker

11. Stable Matching Problem
David Gale
Lloyd Shapley

12. Questions/Comments?

13. 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

14. Simplicity is good

15. 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?

16. Questions/Comments?

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

18. On matchings
Mal
Wash
Simon
Inara
Zoe
Kaylee

19. A valid matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

20. Not a matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

21. Perfect Matching
Mal
Wash
Simon
Inara
Zoe
Kaylee

22. Preferences
Mal
Wash
Simon
Inara
Zoe
Kaylee

23. Instability
Mal
Wash
Simon
Inara
Zoe
Kaylee

24. Questions/Comments?

25. Discuss: Naïve algorithm!

26. 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

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

28. Moral of the story…
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