Lecture 6

CSE 331Sep 10, 2012

Homeworks

HW 1 posted online: see blog/piazza

Pickup graded HW 0 in TA OHs

Suggestions for Piazza

Email them: team “at” piazza “dot” com

Lecture pace

Mid-term

Online Office Hours

Tomorrow: 9:30pm to 10:30pm

Stable Marriage problem

Set of men M and women W

Matching (no polygamy in M X W)

Perfect Matching (everyone gets married)

Instablity

mm ww

m’ w’

Preferences (ranking of potential spouses)

Stable matching = perfect matching+ no instablity

Two Questions

Does a stable marriage always exist?

If one exists, how quickly can we compute one?

Answer both Qs in +ve by the Gale-

Shapley algorithm

Answer both Qs in +ve by the Gale-

Shapley algorithm

Gale-Shapley Algorithm

(er, not Nobel prize winners, at least not yet)

Women do all the proposing (different from the book)

Everyone is in one of three states: free, engaged and married

Step 1: A free woman w proposes to her most preferred man m. (m,w) get engaged

General step: A free woman w proposes to her top unproposed man m.

Questions/Comments?

Gale-Shapley AlgorithmIntially 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

If m is free

(m,w) get engaged

Else (m,w’) are engaged

If m prefers w’ to w

w remains freeElse

(m,w) get engaged and w’ is free

Output the engaged pairs as the final output

Preferences

Mal

Wash

Simon

Inara

Zoe

Kaylee

GS algorithm: Firefly Edition

1

1

2

2

3

3

4

4

5

5

6

6

Mal

Wash

Simon

Inara

Zoe

Kaylee