1. Lecture 12
CSE 331
Sep 27, 2010

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You will have last 5 minutes of the lecture

3. Online Office Hour Wed 9:30-10:30

4. Gale-Shapley Algorithm
At most n2 iterations
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
O(1) time implementation
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

5. Gale-Shapley Algorithm
Linked list of free women
Intially all men and women are free
Array Next[w]
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
Today
If m is free
(m,w) get engaged
Else (m,w’) are engaged
Today
If m prefers w’ to w
w remains free
ManPref[m,j]
WomanPref[w,j]
Else
(m,w) get engaged and w’ is free
Output the engaged pairs as the final output

6. Yes, Firefly again but with numbers1 1 2 2 3 3

7. The data structures so far1 2 3
Man-Pref 1 2 3 1 2 3 1 2 3 1 3
Linked list of free women 2 1 2 3
first 1
Next

8. Implementation Steps (i) How to represent the input?
(ii) How do we find a free woman w?
Init: O(n), Update: O(1)
(iii) How would w pick her best unproposed man m?
Init: O(n), Update: O(1)
(iv) How do we know who m is engaged to?
(v) How do we decide if m prefers w’ to w?

9. Overall running time n2 X ( O(1) + O(1) + Update(iv) + Update(v) )
O(n) + O(n) + Init(iv) + Init(v)
n2 X ( O(1) + O(1) + Update(iv) + Update(v) )

10. Questions?

11. Reading Assignments
Sec 1.1 and Chap. 2 in [KT]

12. Relationship: Mention in other’s program
Graphs
Representation of relationships between pairs of entities/elements
Edge
Entities: News hosts
Relationship: Mention in other’s program
Vertex

13. Graphs are omnipresent
Airline Route maps

14. What does this graph represent?
Internet

15. And this one?
Math articles on Wikipedia

16. And this one?

17. Rest of today’s agenda
Basic Graph definitions