1. Lecture 24 CSE 331 Oct 30, 2009

2. Homework stuff Please turn in your HW 6 Graded HW 5 and HW 7 at the END of the lecture

3. Group talk time Form groups of size at most 4 You should always sit with your group Pick a group leader who is responsible for asking group’s questions The groups and group leader can change from lecture to lecture DO THIS NOW!

4. Dijkstra’s shortest path algorithm Input: Directed G=(V,E), l e ≥ 0, s in V S = {s}, d(s) =0 While there is a v not in S with (u,v) in E, u in S d’(v) = min e=(u,v) in E, u in S d(u)+l e Pick w that minimizes d’(w) Add w to S d(w) = d’(w) s s v v u u z z x x y y 1 2 4 3 3 1 2 1 2 d(s) = 0 1 4 2 s s u u d(u) = 1 4 2 v v d(v) = 2 5 x x d(x) = 2 3 4 y y d(y) = 3 z z d(z) = 4 Shortest paths

5. Couple of remarks The Dijkstra’s algo does not explicitly compute the shortest paths Can maintain “shortest path tree” separately Dijkstra’s algorithm does not work with negative weights Q1 in HW 7

6. Today’s agenda Prove correctness of Dijkstra’s algorithm Efficient implementation of Dijkstra’s algorithm

7. Dijkstra’s shortest path algorithm Input: Directed G=(V,E), l e ≥ 0, s in V S = {s}, d(s) =0 While there is a v not in S with (u,v) in E, u in S d’(v) = min e=(u,v) in E, u in S d(u)+l e Pick w that minimizes d’(w) Add w to S d(w) = d’(w) s s v v u u z z x x y y 1 2 4 3 3 1 2 1 2 d(s) = 0 1 4 2 s s u u d(u) = 1 4 2 v v d(v) = 2 5 x x d(x) = 2 3 4 y y d(y) = 3 z z d(z) = 4 Shortest paths

8. Reading Assignment Sec 4.4 of [KT]