A lot of the
time,
doubling the
speed of your computer will double the amount of
data it can
process over a given
time interval. For instance, if you have a computer that can
crunch through 500
computations of a certain type in ten seconds, and you double the speed of that computer, it should be able to
crunch through 1000
computations of the same type in ten seconds.
Sadly, this is not always true. For NP problems that do not have a known polynomial solution, doubling the speed of the computer will only add a
fixed amount of
computations.
For
example, suppose our 100
MHz machine can process 500 units of data in 10 seconds. The 200 MHz machine will not necessarily be able to handle 1000 units. It may only be able to handle 550. To be able to handle 600, we would need a 400 MHz machine and so on.
Units Speed
500 100 MHz
550 200 MHz
600 400 MHz
650 800 MHz
700 1.6 GHz
750 3.2 GHz
800 6.4 GHz
As you might see,
solving a signifigantly large problem (one million units for instance) is going require a computer faster than the combined speeds of all computers in
existence.
If
P were equal to NP (Though unlikely) that would mean that there does in fact exist some
algorithm which would be able to handle the problem in
polynomial time.