1. Lecture 24
CSE 331
Oct 29, 2018

2. Mini Project video due in 1 week

3. Peer Evaluation Survey
Some more details by Tuesday

4. HW 5 grading delayed (more)
New plan to get it done by tonight

5. Re-grade deadlines

6. Mid-term temp grades

7. One-on-one meeting slots

8. Shortest Path Problem

9. Another more important application
Is BGP a known acronym for you?
Routing uses shortest path algorithm

10. Shortest Path problem s 100 Input: Directed graph G=(V,E) w15 5 s u w
100
Input: Directed graph G=(V,E)
Edge lengths, le for e in E
“start” vertex s in V 15 5 s u w 5 s u
Output: Length of shortest paths from s to all nodes in V

11. Dijkstra’s shortest path algorithm
E. W. Dijkstra ( )

12. Towards Dijkstra’s algo: part ek
Determine d(t) one by one s
d(s) = 0 u x y

13. Towards Dijkstra’s algo: part do
Determine d(t) one by one s
Let u be a neighbor of s with smallest l(s,u) 3 4
100 u x y
d(u) = l(s,u)
Not making any claim on other vertices

14. Towards Dijkstra’s algo: part teen
Determine d(t) one by one R
Assume we know d(v) for evert v in R s u x y w
Compute an upper bound d’(w) for every w not in R
d(w)
d(u) + l(u,w)
d(w) d(x) + l(x,w)
d’(w) = min e=(u,w) in E, u in R d(u)+le
d(w) d(y) + l(y,w)

15. Dijkstra’s shortest path algorithm1
d’(w) = min e=(u,w) in E, u in R d(u)+le 1 2 4 3 y 4 3 u
d(s) = 0
d(u) = 1 s x 2 4
d(w) = 2
d(x) = 2
d(y) = 3
d(z) = 4 w z 5 4 2 s w
Input: Directed G=(V,E), le ≥ 0, s in V u
R = {s}, d(s) =0
Shortest paths x
While there is a x not in R with (u,x) in E, u in R z y
Pick w that minimizes d’(w)
Add w to R
d(w) = d’(w)

16. 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
Left as an exercise

17. Rest of Today’s agenda Prove the correctness of Dijkstra’s Algorithm
Runtime analysis of Dijkstra’s Algorithm