Question

Generalize the hierarchical network in Figure 7.27 so that the $2^K$ nodes are interconnected in a full mesh at the top of the hierarchy and so that each node connects to two $2^L$ nodes in the next lower level in the hierarchy. Suppose there are four levels in the hierarchy. a. How many nodes are in the hierarchy? b. What does a routing table look like at level $j$ in the hierarchy, $j=1,2,3$, and 4 ? c. What is the maximum number of hops between nodes in the network?

    Generalize the hierarchical network in Figure 7.27 so that the $2^K$ nodes are interconnected in a full mesh at the top of the hierarchy and so that each node connects to two $2^L$ nodes in the next lower level in the hierarchy. Suppose there are four levels in the hierarchy.
a. How many nodes are in the hierarchy?
b. What does a routing table look like at level $j$ in the hierarchy, $j=1,2,3$, and 4 ?
c. What is the maximum number of hops between nodes in the network?

Communication Networks: Fundamental Concepts and Key Architectures

Indra Widjaja,… 1st Edition

Chapter 7, Problem 34

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Step 1

The number of nodes in the hierarchy can be calculated as follows: At the top level, there are $2^K$ nodes. At the next level, each of the $2^K$ nodes connects to $2^L$ nodes, so there are $2^K \times 2^L$ nodes. At the next level, each of the $2^K \times 2^L$ Show more…

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Generalize the hierarchical network in Figure 7.27 so that the $2^K$ nodes are interconnected in a full mesh at the top of the hierarchy and so that each node connects to two $2^L$ nodes in the next lower level in the hierarchy. Suppose there are four levels in the hierarchy. a. How many nodes are in the hierarchy? b. What does a routing table look like at level $j$ in the hierarchy, $j=1,2,3$, and 4 ? c. What is the maximum number of hops between nodes in the network?

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