Problem set 4 (Tuesday 20.11.2001)

1. Assuming that alla routers and hosts are working properly and that all software in both is free of all errors, is there any chance, however small, that a packet will be delivered to the wrong destination?

2. Consider one sender and 32 receivers. Suppose the sender is connected to the receivers through a binary tree of routers. The sender is the root and the receivers are the leaves in the tree and in each node between has a router. The sender sents a packet first to the next router, that sends it to the router below etc until the packet reaches the the receiver.
   1. How many sendings alltogether are needed if a separate packet is sent to each receiver?
   2. How many sendings are needed, if the packet is sent as a multicast packet to each receiver?

3. The topology of the network is given below. A, B and C are networks of different service providers (ISP) and x, y and z normal company networks. The BGP (Border Gateway Protocol)is used for routing between networks.

   
   

   
   

   Network x, although connected to two provider networks, doesn't want to relay packets between those networks. The service providers relay traffic from other service providers only to their own customers. For example network X wants from A only that traffic going to x, but doesn't not want to relay traffic going to y.
   1. What kind of path information do the BGP routers of these networks exchange with each others, ie. what routes they reveal to the other networks?
   2. Based on the information available, networks x, y and z form each their own view of the network topology. What are the topology views of the x, y and z?

4. Suppose node C is chosen as the center in a center-based multicast routing algorithm. Assuming that each attached router in the multicast group (= A, B, E and F) uses its least-cost path to node C, show the resulting center-based multicast routing tree. Is the resulting tree a minimum-cost Steiner tree?

            1             1
          B ------------ D ------------ E
          | .                          .|
          |  .                       .  |
          |   .                    .    |
          |    . 2             2 .      |
        4 |     .              .        | 1
          |      .           .          |
          |       .        .            |
          |        .     .              |
          |         .  .                |
          A -------- C ---------------  F            
               3             2
   
   

5. Supposing that in the net of the previous problem the cost of the link BD becomes tenfold, that is changes to 10. Find the Steiner tree that connects all the nodes A, B, E and F belonging to the group. It is not necessary to use the Steiner tree construction algorithm. It is enough to inspect the net in order to find the Steiner tree.

6. Consider the network below. Supposing that the link costs are equal on all links, what kind of "reverse path forwarding" -tree would you make for node F? How is this tree actually formed? When node F sends a broadcast packet, how many packets are really sent in the subnetwork?

   
                B --------------------------------------------- C
                |                                               |
         E -----|---------------------------- A                 |
         |      |                             |                 |
         |      |                             |                 |  
         H -----|------------ I ------------- F --------------- D
         |      |             | .                               |
         |      L             |  .                              |
         |     .              |   .                             |
         |    .               |    .                            | 
         |   .                |     .                           |
         |  .                 |      .                          |
         | .                  |       .                         |
         |.                   |        .                        |
         K -------- M ------- N -- O -- J --------------------- G