Lecture 10 CSE 331 Sep 22, 2009

Acceptable formats for blog posts Plain text LaTeX HTML

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 At most n 2 iterations O(1) time implementation

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 Linked list of free women Array Next[w] Array Current[m] Up Next ManPref[m,j] WomanPref[w,j] ManPref[m,j] WomanPref[w,j]

Does m prefer w’ to w? Option 1: m searches through ManPref[m] O(n) time! Define array Ranking[m,w] Initialization? O(n 2 ) time Update?

Reading Assignments Section 2.4 in [KT] Section 2.5 in [KT] Ask Jeff/me if you have questions

Questions?

Graphs Representation of relationships between pairs of entities/elements Entities: News hosts Relationship: Mention in other’s program Entities: News hosts Relationship: Mention in other’s program Vertex Edge

Graphs are omnipresent Airline Route maps

What does this graph represent? Internet

And this one? Math articles on Wikipedia

And this one?

Today’s agenda Basic Graph definitions