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s8 - Compen/EE 362 Asst 8 Solution Fall 2010 T ext Problem...

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Compen/EE 362 Asst. 8 Solution Fall 2010 Problem 1. Text Problem 5.8. Give a simple heuristic for finding two paths through a network from a given source to a given destination that can survive the loss of any communication line (if two such paths exist. Don’t worry about possibility of router crashes. Give two answers. In one, the answer if one of the alternatives is the least cost path and the other is as good as possible. In the other answer, don’t worry about how good the two paths are. Solution. First case: Pick the least cost route and remove all lines used for the route from A to B. Then run the shortest path algorithm to find the shortest path for this reduced network, if there is such a path. Even if there is no path after the least cost path is removed, it still is possible to find two paths. In general, assume there is at least one path from A to B. To see if two paths are possible, try to draw a cut that isolates A and B by cutting only one link. If and only if you can find such a cut, only one path is possible.
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Assume all cuts pass through 2 or more links.
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