Routers

Question

Consider a network with hierarchical routing with 5760 routers. r region and c cluster sizes should be chosen to minimize the size of the routing table for a three-layer hierarchy. What is the minimum size of table?

Ans is given as 36.

Please provide solution .

Answer 1

For this type of questions I follow a simple trick , no need of options in this and surely you get verified answer.

Step 1: find the cube root of given total number of routers.

Cube root(5760) = 17.96

On dividing 5700 by 17 or 18 we couldn't find a perfect number whereas on going with 16 we will find a solution . (You can go on increasing the number but rather I suggest to check for number in close proximity of cube root)

5760/16 = 360

Step 2: find the square root this number

Sqrt(360) = 18.97

Again on doing division by 18 only we will find

360/18 = 20

Now we have three numbers {16, 18, 20}

We know the relationship as

Number (clusture) < Number(regions) < Number(routers)

So we have

# of clustures = 16

# of regions = 18

# of routers = 20

Size of the table = 16+18+20

                            =54

@Arjun sir please varify my answer if there is any mistake.