Lecture 8 CSE 331 Sep 17, 2010. HW 1 due today Place Q1 and Q2 in separate piles I will not accept HWs after 1:15pm.

Lecture 8

CSE 331Sep 17, 2010

HW 1 due today

Place Q1 and Q2 in separate piles

I will not accept HWs after 1:15pm

HW 1 solutions

At the end of the lecture

HW 2 has been posted

harder than HW 1, so start early!

Return signed forms

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

≤ n2 iterations of the while loopIntially 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

Each iteration has one proposal

Each iteration has one proposal

Each proposal is newEach proposal is new

# iterations≤

# proposals≤

# pairs (m,w)≤n2

# iterations≤

# proposals≤

# pairs (m,w)≤n2

Today’s lecture

GS algorithms always outputs a stable marriage

Observation 1Intially 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

Once a man gets engaged, he remains engaged (to “better”

women)

Once a man gets engaged, he remains engaged (to “better”

women)

Observation 2Intially 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

If w proposes to m after m’, then she prefers m’

to m

If w proposes to m after m’, then she prefers m’

to m

Questions/Comments?

HW 1 due today

Place Q1 and Q2 in separate piles

I will not accept HWs after 1:15pm

Proof technique de jour

Source: 4simpsons.wordpress.com

Proof by contradiction

Assume the negation of what you want to proveAssume the negation of what you want to prove

After some reasoning

After some reasoning

Claim: GS algo outputs a matching