In Problem below, if the destination node is located at 5 hops apart from a given source node, what is the maximum possible value of

(a) The number of alternate paths of length of 5 hops?
(b) Alternate disjoint paths of length 5 hops?

If the updated message is sent every 5 seconds, what is the upper limit on the number of messages initiated periodically if a table-driven routing protocol is to be used? Explain clearly


(a) Alternate paths means a source node S can take A-B-C to destination D, it also

can take M-L-N to destination D if the formal link fails. If the destination node is

located at 5 hops apart from a given source node, every node is connected to

exactly 4 adjacent node, therefore, source can connect with four adjacent node,

among these four adjacent nodes, every node mostly can connect with another 3

nodes, then from 4 nodes arrive to destination. Therefore, there would be

4*3*3*1*1 = 36 alternate paths (maximum).







(b) For disjoint-ness, no intermediate node should be common among the paths.

One simple way is to have a unique path between 12 nodes after 2 links from

either source or destination, giving 4 x3x1x4 = 48 disjoint paths (maximum).

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