1. E&CE 418: Tutorial-10
Instructor: Prof. Xuemin (Sherman) Shen
TA: Ning Zhang
Office Hours: Tue. 1:00pm - 3:00pm or by appointment

2. Problem 1

3. Problem 1

4. Problem 2
The number shown in the following figure is the probability of the link failing during the lifetime of a virtual circuit from node A to node B. It is assumed that links fail independently of each other.
(a) Find the most reliable path from A to B, i.e., the path for which the probability that all links stay intact during the virtual circuit’s lifetime is maximal.
(b) Find the second most reliable path from A to B which does not share any link belonging to the path found in (a).

6. The Bellman-Ford algorithm:
Label each node i with (di, j) where di is the distance from node i to the destination node through the neighboring node j.
Initialization: label node i with (di0,.) where
Shortest distance labeling of all nodes: for each successive run h > 0, determine j which minimizes dih+1=d(i,j)+djh, and update label at each node i with (dih+1,j).
Repeat step 3 until no change of any di occurs.

8. (b) Find the second most reliable path from A to B which does not share any link belonging to the path found in (a).
The second most reliable path from A to B that does not share any link belonging to the shortest path can be found by: first remove all links passing by the shortest path from the diagram, then find the shortest path from the residue diagram. The residue diagram is as follows:

9. From the table, we can the second shortest path is A → 5 → 3 → 2 → B.

10. Problem 4

11. Problem 4

12. Problem 4

13. Problem 4

14. Problem 3

15. Thanks !