Chapter 16.4, Problem 9WE

To determine

To find: The computer that can send data to the most points via one relay.

Answer to Problem 9WE

The computer $B$ can send data to the most points via one relay.

Explanation of Solution

Given information:

Computer $A$ sends data to computer B. computer $B$ sends and receives data from computers $A,C$ and $D$ . Computer $E$ receives data from computer $C$ and $D$ .

Let $X$ be the matrix.

The arrows in the diagram shows the direction in which data can be transmitted and received. The rows of matrix represented the directions of the data transmitted and the columns represent the data to be received. Use $1$ if direct transmission is possible and $0$ if it is not possible.

The matrix is,

  $X=\left[\begin{array}{l}01000\\ 10110\\ 01001\\ 01001\\ 0000\text{}0\end{array}\right]$ .

The number of routes data can be sent from one point to another using exactly one relay is $X^2$ .

  $\begin{array}{c}{X}^2=\left[\begin{array}{l}01000\\ 10110\\ 01001\\ 01001\\ 0000\text{}0\end{array}\right]\left[\begin{array}{l}01000\\ 10110\\ 01001\\ 01001\\ 0000\text{}0\end{array}\right]\\ =\left[\begin{array}{c}10110\\ 03002\\ 10110\\ 10110\\ 00000\end{array}\right]\end{array}$

In the above matrix we can see that the second row contains the greatest element.

Therefore, computer $B$ can send data to the most points via one relay.