Question #$2$Serverless Data Analytics $(2$ Pts$.)$

Try to answer the following questions the best you can:

$1.$ It is still under scrutiny whether data analytics can be efficiently run atop a serverless architecture. However, several attempts

have been successful for embarrassingly parallel workloads and problems $($e$.$g$.,$ PyWren$).$ One of those problems is large$-$scale

matrix multiplication. Given two square matrices of N x N elements, standard matrix multiplication takes $($N$3)$ time. For N

large $($e$.$g$.,$ matrices of $100$GBs$),$ no laptop or server can hold in memory such an amount of data, so more than a single

machine is needed.

The goal of this task is to provide a solution for such a problem by combining a FaaS offering $($e$.$g$.,$ AWS Lambda$)$ and an

object store $($e$.$g$.,$ Amazon S$3).$ Initially, both matrices are stored in Amazon S$3.$ The result matrix must be written back to S$3.$

Provide a high$-$level description of your solution for N $=40,000$ double$-$precision elements. Hence, a matrix of N x N occupies

$11\mathrm{.}92$GB of memory. For simplicity, you can assume that each function has been allocated $1$GB of memory. Graphically, the

architecture of the system may be described as follows: