Clearly this route will be one of ns links but we can

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.

Ask a homework question - tutors are online