E&CE 418: Tutorial-10 Instructor: Prof. Xuemin (Sherman) Shen TA: Ning Zhang Email:...
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Transcript of E&CE 418: Tutorial-10 Instructor: Prof. Xuemin (Sherman) Shen TA: Ning Zhang Email:...
E&CE 418: Tutorial-10
Instructor: Prof. Xuemin (Sherman) ShenTA: Ning Zhang
Email: [email protected] Hours: Tue. 1:00pm - 3:00pm or by appointment
1
Problem 1
Problem 1
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).
Problem 2
The Bellman-Ford algorithm:
1. Label each node i with (di, j) where di is the distance from node i to the destination node through the neighboring node j.
2. Initialization: label node i with (di0,.) where
3. Shortest distance labeling of all nodes: for each successive run h > 0, determine j which minimizes di
h+1=d(i,j)+djh, and update label at each
node i with (dih+1,j).
4. 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 !