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Unformatted text preview: een any two
nodes, and in particular between n and every other node.) There are three kinds of nodes
in the shortest path tree:
1. n itself: the route from n to n is not a link, and we will call it “Self”.
2. A node v directly connected to n in the tree, whose parent is n. For such nodes, the
route is the link connecting n to v . SECTION 18.6. SUMMARY 13 3. All other nodes, w, which are not directly connected to n in the shortest path tree.
For such nodes, the route to w is the same as the route to w’s parent, which is the
node one step closer to n along the (reverse) path in the tree from w to n. Clearly,
this route will be one of n’s links, but we can just set it to w’s parent and rely on the
second step above to determine the link.
We should also note that just because a node w is directly connected to n, it doesn’t
imply that the route from n is the direct link between them. If the cost of that link
is larger than the path through another link, then we would want to use the route
(outgoing link) corresponding to that better path. 18.6 Summary This lecture discussed network routing in the absence of failures. The next lecture will look
at how to make routing work even when links and nodes fail. Acknowledgments Thanks to Sari Canelake and Katrina LaCurts for many helpful comments, and to Fred
Chen and Eduardo Lisker for bug ﬁxes. Problems and Questions
1. Consider the network shown in Figure 18-7. The number near each link is its cost.
We’re interested in ﬁnding the shortest paths (taking costs into account) from S to
every other node in the network.
What is the result of running Dijkstra’s shortest path algorithm on this network? To
answer this question, near each node, list a pair of numbers: The ﬁrst element of the
pair should be the order, or the iteration of the algorithm in which the node is picked.
The second element of each pair should be the shortest path cost from S to that node.
2. Alice and Bob are responsible for implementing Dijkstra’s algorithm at the nodes in...
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.
- Fall '13