Q18,Paper 2,J 13.In hierarchical routing with 4800 routers, what region and cluster sizes should be chosen to minimize the size of the routing table for a three-layer hierarchy ?

(A) 10 clusters, 24 regions and 20 routers

(B) 12 clusters, 20 regions and 20 routers

(C) 16 clusters, 12 regions and 25 routers

(D) 15 clusters, 16 regions and 20 routers

Explanation.

Assume that there are 'a' clusters, 'b' regions in each region and 'c' routers per region. 

And  a.b.c=4800. All the options qualify multiplication.

The formula to minimize is (a - 1) + (b - 1) + c.  eq 1.

Option 1.  Eq 1 sums 52.

Option 2, sums 50.

Option 3.sums 51.

Option 4.  Sums 49.

Answer D will have to keep minimum routing table.