CMPEN/EE 362
Asst. 9 Solution
Spring 2009
Problem 1.
Text Problem 5.8. 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.
Then
run the shortest path algorithm to find the shortest path for this reduced network, if there
is such a path. The two paths have no two lines in common (it is OK if they have a router in
common), so a failure in any line of one path will not affect the other.
Second case.
If there is no second path after the least cost is removed, there still
may be two routes, but neither is least cost. Example:
Removing the least cost route (cost 4) lines from A to B disconnects A and B. But there are
two paths with no common lines, with path costs 9 each. As long as there is no cut between
A and B which divides the network in two parts with only one connecting link, the problem
is solvable for the second case.
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 Spring '09
 JOHNMETZNER
 Shortest path problem, minimum hop, minimum hop sink, minimum hop source, hop sink tree, hop source tree

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