Programmers at a software company work on
personal computers interconneted
so that they can all transfer files from one computer
to the others.
Below are different ways of connecting four computers.
All the computers are connected to a computer
referred to as "the central computer."
Every computer is directly connected to all the others.
Every computer is connected to a nearby computer. A message
from a computer to one that is not directly conected to it passes
through intermediary computers.
The computers are connected in a circle. A message
from a computer to one that is not directly connected to it passes through intermediary
computers along the shortest path possible.
Compare different ways of connecting computers
Compare the above methods of connecting any number of computers from the following perspectives:
The time it takes to send a message from one computer to another.
Passing a message from a computer to one connected to it takes one second. How does the method of connection
affect the maximum time it takes to send a message between two computers?
Effect of a broken link. If a connection between two computers is down, how
is the functioning of the network affected in each method of connection?
Effect of a broken computer.
Cost. Connecting each pair of computers
costs money. How does the total network cost depend on the number of
computers in each method of connection? Represent this dependence
with a graph, a value table, and a correspondence rule.