1. Lecture 28 CSE 331 Nov 5, 2010

2. HW 7 due today Q1 in one pile and Q 2+3 in another I will not take any HW after 1:15pm

3. Graded HW 6 + HW 7 solutions On Monday

4. HW 8 posted

5. Kruskal’s Algorithm Joseph B. Kruskal Input: G=(V,E), c e > 0 for every e in E T = Ø Sort edges in increasing order of their cost Consider edges in sorted order If an edge can be added to T without adding a cycle then add it to T

6. Prim’s algorithm Robert Prim Similar to Dijkstra’s algorithm Input: G=(V,E), c e > 0 for every e in E 2 1 3 51 50 0.5 S = {s}, T = Ø While S is not the same as V Among edges e= (u,w) with u in S and w not in S, pick one with minimum cost Add w to S, e to T 2 1 50 0.5

7. Any questions?

8. Reverse-Delete Algorithm Input: G=(V,E), c e > 0 for every e in E T = E Sort edges in decreasing order of their cost Consider edges in sorted order If an edge can be removed T without disconnecting T then remove it 2 1 3 51 50 0.5 2 1 3 51 50 0.5

9. (Old) History of MST algorithms 1920: Otakar Borůvka 1930: Vojtěch Jarník 1956: Kruskal 1957: Prim 1959: Dijkstra Same algo!

10. HW 7 due today Q1 in one pile and Q 2+3 in another I will not take any HW after 1:15pm

11. Today’s agenda Optimality of Kruskal’s and Prim’s algorithms