Lecture 24
CSE 331
Oct 30, 2009

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

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

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

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

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

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

Reading Assignment
Sec 4.4 of [KT]