For each of the topologies of Fig. 8-16, what is the diameter of the interconnec

Question

For each of the topologies of Fig. 8-16, what is the diameter of the interconnection network?
Count all hops (host-router and router-router) equally for this problem.

Please type answer do not hand write. Thank you very much.

Interconnection Technology Each node has a network interface card with one or two cables (or fibers) com ing out of it.These cables connect either to other nodes or to switches. In a small system, there may be one switch to which all the nodes are connected in the star topologv of Fig. 8-16(a). Modern switched Ethernets use this topology. Figure 8-16. Various interconnect topologies. (a) A single switch. (b) A ring. (c) A grid. (d) A double torus. (e) A cube. (f) A 4D hypercube.

Explanation / Answer

After calculating shortest distance between any two nodes, Diameter is the shortest distance between most distance nodes in the network.

Diameter for star network: 2 (Any 2 nodes are connected through interconnecting device)

Diameter for Ring network: n/2. (n = number of nodes. any far away nodes are reached by travelling n/2 hopes)

Diameter for Grid network: 2(n1/2-1 )

Diameter of double torus :n1/2

Diameter of cube: log n

Diameter of 4D-hypercube: log N+1 (two analogus nodes of two cubes are directlly connected. hence diameter of cube = log n and diameter of 4d-hypercube is log n +1)

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