Lecture02_buaa - Announcements CSE 421 Algorithms Richard...

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1 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, 2:30-3:20 pm, Friday, 2:30-3:20 pm. • Ning’s office hours: – Monday, 12:30-1:20 pm, Tuesday, 4:30-5:20 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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Lecture02_buaa - Announcements CSE 421 Algorithms Richard...

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