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Destination
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? Each link has a cost of either 1 or 2 and link costs are symmetric (the cost from X
to Y is the same as the cost from Y to X ). The routing table entries correspond to
minimumcost routes.
(a) Draw a network topology with the smallest number of links that is consistent with
the routing table entries shown above and the cost information provided. Label
each node and show each link cost clearly.
(b) You know that there could be other links in the topology. To ﬁnd out, you now
go and inspect D’s routing table, but it is mysteriously empty. What is the smallest possible value for the cost of the path from D to F in your home network
topology? (Assume that any two nodes may possibly be directly connected to
answer this question.)
6. A network with N nodes and N bidirectional links is connected in a ring as shown
in Figure 194, where N is an even number. The network runs a distancevector
protocol in which the advertisement step at each node runs when the local time is
T ∗ i seconds and the integration step runs when the local time is T ∗ i + T seconds,
2
(i = 1, 2, . . .). Each advertisement takes time δ to reach a neighbor. Each node has a
separate clock and time is not synchronized between the different nodes.
Suppose that at some time t after the routing has converged, node N + 1 is inserted
into the ring, as shown in the ﬁgure above. Assume that there are no other changes SECTION 19.9. SUMMARY: COMPARING LINKSTATE AND VECTOR PROTOCOLS 13 Figure 194: The ring network with N nodes (N is even). in the network topology and no packet losses. Also assume that nodes 1 and N
update their routing tables at time t to include node N + 1, and then rely on their
next scheduled advertisements to propagate this new information.
(a) What is the minimum time before every node in the network has a route to node
N + 1?
(b) What is the maximum time before every node in the network has a route to
node N + 1?
7. Alyssa P. Hacker manages MIT’s internal network that runs linkstate routing. She
wants to experiment with a few possible routing strategies. Listed below are the
names of four strategies and a brief description of what each one does.
(a) MinCost: Every node picks the path that has the smallest sum of link costs along
the path. (This is the minimum cost routing you implemented in the lab).
(b) MinHop: Every node picks the path with the smallest number of hops (irrespective of what the cost on the links is).
(c) SecondMinCost: Every node picks the path with the second lowest sum of link
costs. That is, every node picks the second best path with respect to path costs.
(d) MinCostSquared: Every node picks the path that has the smallest sum of
squares of link costs along the path.
Assume that sufﬁcient information is exchanged in the link state advertisements, so
that every node has complete information about the entire network and can correctly
implement the strategies above. You can also assume that a link’s properties don’t
change, e.g., it doesn’t fail.
(a) Help Alyssa ﬁgure out which of these strategies will work correctly, and which
will result in routing with loops. In case of strategies that do result in routing loops, come up with an example network topology with a routing loop to
convince Alyssa.
(b) How would you implement MinCostSquared in a distancevector protocol?
Specify what the advertisements should contain and what the integration step
must do....
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.
 Fall '13
 HariBalakrishnan

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