1. Lecture 24
CSE 331
Oct 25, 2013

2. Homeworks
HW 6 posted on piazza
Graded HW5 pickup from Monday

3. Mini Project report Due Nov 6

4. Shortest Path Problem

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

6. 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: All shortest paths from s to all nodes in V

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

8. 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)

9. 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

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

11. Reading Assignment
Sec 4.4 of [KT]

12. Building a fiber network
Lay down fibers to connect n locations
All n locations should be connected
Laying down a fiber costs money
What is the cheapest way to lay down the fibers?