Lecture 6 CSE 331 Sep 10, 2012

Homeworks HW 1 posted online: see blog/piazza Pickup graded HW 0 in TA OHs

Suggestions for Piazza 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 m m w w m’m’w’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

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 Algorithm 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 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

Preferences Mal Wash Simon Inara Zoe Kaylee

GS algorithm: Firefly Edition Mal Wash Simon Inara Zoe Kaylee