In hierarchical routing with 4800 routers, what region and cluster sizes should be chosen to minimize the size of the routing table for a threelayer hierarchy ?
UGC NET - 2013,
Answer: D
For three level hierarchical routing the routing table has one entry for each cluster, one for each region of the local cluster and one for each router of the local region, so its size is the sum of the three numbers, while their product must equal the 4800 routers. Option (A) 10 x 24 x 20 = 4800 gives a table of 54, option (B) 12 x 20 x 20 = 4800 gives 52, option (C) 16 x 12 x 25 = 4800 gives 53, and option (D) 15 x 16 x 20 = 4800 gives 51. All four have the right product, and the smallest sum is 51 for 15 clusters, 16 regions and 20 routers, option (D). The sum is smallest when the three factors are as nearly equal as possible, near the cube root of 4800 which is about 16.9.
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