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CSE 421
Algorithms
Richard Anderson
Autumn 2006
Lecture 2
Announcements
• It’s on the web.
• Homework 1, Due October 4
– It’s on the web
• Subscribe to the mailing list
• Richard’s office hours:
– Tuesday, 2:303:20 pm, Friday, 2:303:20 pm.
• Ning’s office hours:
– Monday, 12:301:20 pm,
Tuesday, 4:305:20 pm.
A closer look
• Stable matchings are
not necessarily fair
m
1
:
w
1
w
2
w
3
m
2
:
w
2
w
3
w
1
m
3
:
w
3
w
1
w
2
w
1
:
m
2
m
3
m
1
w
2
:
m
3
m
1
m
2
w
3
:
m
1
m
2
m
3
m
1
m
2
m
3
w
1
w
2
w
3
How many stable matchings can you find?
Algorithm under specified
• Many different ways of picking m’s to propose
• Surprising result
– All orderings of picking free m’s give the same result
• Proving this type of result
– Reordering argument
– Prove algorithm is computing something mores
specific
• Show property of the solution – so it computes a specific
stable matching
Proposal Algorithm finds the best
possible solution for M
• Formalize the notion of best possible solution
• (m, w) is valid if (m, w) is in some stable
matching
• best(m): the highest ranked w for m such that
(m, w) is valid
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 Fall '06
 RichardAnderson
 Algorithms, Cauchy distribution

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