c) Given graph G=(N,E), where N is the set of routers and E is the set of links. Using Dijkstra's link-state routing algorithm compute the least cost path from node U to all other nodes and show the resulting least-cost-path tree from U. Show all calculations to get full credit. 1 2 3 4

A collection of 2" stations uses the adaptive tree walk protocol to arbitrate access to a shared cable. At a certain instant, two of them become ready. What are the minimum, maximum, and mean number of slots to walk the tree if 2" >>1?

Distance-Vector and link state are two popular algorithms that have been implemented by RIP and OSPF for intra-domain routing. Summarize the differences between the two approaches.

What is B’s new routing table? (proof is needed)

A collection of 2" stations uses the adaptive tree walk protocol to arbitrate access to a shared cable. At a certain instant, two of them become ready. What are the minimum, maximum, and mean number of slots to walk the tree if 2" >>1?

Consider the distance vector routing count-to-infinity problem. Is it possible to have a count-to-infinity problem if the cost of a connection is reduced? Why? How about joining two nodes that aren't connected?

Computer Science 5. Using Dijkstra's algorithm, generate a least-cost route to all other nodes for node A of the following figure. Display the results in the following table. 3 4. E Iteration 1. T L(B) Path L(C) Path L(D) Path L(E) Path L(F) Path {A}

Consider the network shown in the figure below, and assume that each node initially knows the costs to each of its neighbors. If the distance-vector algorithm is used by all the routers, what would be the distance table entries at node E?

5. For the graph below: 7 5 9 20 3. 1 1 1 3 (Route length is the sum of the weights of the edges in the route. When no weight is assigned to an edge the weight is assumed to be 1.) What is the shortest route from 5 to 5 to 2?

8. Consider the 6-node network shown below, with the given link costs. Using Dijkstra's algorithm, find the least cost path from source node U to all other destinations: u 8 9 6 6 V X 9 W 6 D Z a. What is the shortest distance to node w and what node is its predecessor? Write your answer as n,p b. What is the shortest distance to node v and what node is its predecessor? Write your answer as n,p c. What is the shortest distance to node y and what node is its predecessor? Write your answer as n,p