Project ForgeComputer Networks
OSI/TCP-IP Layers & Routing
GATE 2019
Hard
Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches. Assume that these switches do not have any separate uplink ports. The minimum number of switches needed is
3
Explanation
With S switches (8 ports each, all usable for either machines or inter-switch links), connecting them all together (a spanning tree of switches) needs S−1 inter-switch links, using 2(S−1) ports. Feasibility: 15 + 2(S−1) ≤ 8S → 13 ≤ 6S → S ≥ 2.17, so S≥3. S=3 works: e.g. 3 switches in a chain (2 inter-switch links, using 4 ports), leaving 20 ports for machines — more than enough for 15.
Source: GATE CS 2019 (Set-2) (2019)
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