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consider a general topology (that is, not the specific network shown above) and a synchronous version of the distance-vector algorithm. suppose that at each iteration, a node exchanges its distance vectors with its neighbors and receives their distance vectors. assuming that the algorithm begins with each node knowing only the costs to its immediate neighbors, what is the maximum number of iterations required before the distributed algorithm converges? justify your answer.

Respuesta :

The overall topology is taken into account.

  • The synchronous distance-vector algorithm is used to compute the distance table entries.
  • The network nodes have limited information about their neighbors.
  • Only their neighbors' costs are known to them.

The maximum number of algorithm iterations required for convergence could be computed as follows:

Each iteration, the network nodes exchange distance table information with their neighbors.

Following the very first iteration, all neighbors towards the current node would be aware of the shortest path cost to the current node. Assume that X and Y represent the two nodes that are neighbors. After the first iteration, all of Y's neighbors will be aware of the shortest path cost to node X.

  • Assume that d (the network's diameter) is the length of a longest path in between two nodes in the network with no loops.
  • According to the analogy above, after d-1 iterations, all nodes will know the shortest path cost of d for all other nodes.
  • If the path length exceeds d hops, the path contains loops. The elimination of loops reduces the algorithm lead to no more than d-1 iterations.
  • Any path with more than d hops is made up of loops, causing the algorithm's output to converge in at most d-1 iterations.

As a result, the distance vector algorithm's output converges in at, most d-1 iterations.

To learn more about topology, visit: https://brainly.com/question/14560531

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