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network running a linkstate protocol. On her nodes, Alice implements a minimumcost algorithm. On his nodes, Bob implements a “shortest number of hops” algorithm. Give an example of a network topology with 4 or more nodes in which a
routing loop occurs with Alice and Bob’s implementations running simultaneously
in the same network. Assume that there are no failures.
(Note: A routing loop occurs when a group of k ≥ 1 distinct nodes, n0 , n1 , n2 , . . . , nk−1
have routes such that ni ’s nexthop (route) to a destination is ni+1 mod k .)
3. Consider any two graphs(networks) G and G that are identical except for the costs
of the links.
(a) The cost of link l in graph G is cl > 0, and the cost of the same link l in Graph G
is kcl , where k > 0 is a constant. Are the shortest paths between any two nodes
in the two graphs identical? Justify your answer. CHAPTER 18. NETWORK ROUTING  I 14 WITHOUT ANY FAILURES 2 B
Order: __
Cost: __ C
Order: __
Cost: __ 2 S
Order: 0
Cost: 0 2 3 A
Order: 1
Cost: 2 1 1
E
Order: __
Cost: __ 5 D
Order: __
Cost: __ Figure 187: Topology for problem 1. (b) Now suppose that the cost of a link l in G is kcl + h, where k > 0 and h > 0
are constants. Are the shortest paths between any two nodes in the two graphs
identical? Justify your answer.
4. Eager B. Eaver implements distance vector routing in his network in which the links
all have arbitrary positive costs. In addition, there are at least two paths between
any two nodes in the network. One node, u, has an erroneous implementation of
the integration step: it takes the advertised costs from each neighbor and picks the
route corresponding to the minimum advertised cost to each destination as its route
to that destination, without adding the link cost to the neighbor. It breaks any ties
arbitrarily. All the other nodes are implemented correctly.
Let’s use the term “correct route” to mean the route that corresponds to the
minimumcost path. Which of the following statements are true of Eager’s netw...
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 Fall '13
 HariBalakrishnan

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