E&CE 418: Tutorial-10 Instructor: Prof. Xuemin (Sherman) Shen TA: Ning Zhang Email: n35zhang@uwaterloo.ca Office Hours: Tue. 1:00pm - 3:00pm or by appointment

Problem 1

Problem 1

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).

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.

(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:

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

Problem 4

Problem 4

Problem 4

Problem 4

Problem 3

Thanks !