Question

A datacenter has 10 servers and 4 routers, which they want to connect. Each server and each router can have any number of cables attached to it. Suppose that they would like the connections to satisfy the following property: at any given time, if no more than 4 servers are transmitting data, then each server can transmit via a separate router. For that, they want every (sub)set of 4 to have cables going to all four routers. What is the minimal number of cables needed to achieve this, and how the servers and routers should be connected in this case? Prove both that your scheme satisfies the condition that every set of 4 servers has cables to all routers, and that the number of cables you used is indeed minimal. Use the PigeonHole Principle to prove minimality.

Answer 1

Data centers are much bigger than they were a decade ago, with application requirements vastly different from the traditional client–server applications, and with deployment speeds that are in seconds instead of days. This changes how networks are designed and deployed.

Modern data centers evolved primarily from the requirements of web-scale pioneers such as Google and Amazon. The applications that these organizations built—primarily search and cloud—represent the third wave of application architectures. The first two waves were the monolithic single-machine applications, and the client–server architecture that dominated the landscape at the end of the past century.