# Cowboy ProgrammingGame Development and General Hacking by the Old West

## March 18, 2008

### Exponential Optimizing, or not.

Filed under: Game Development — Mick West @ 9:57 am

I wrote an article titled “Exponential Optimizing” for Game Developer, and since it was published a few people wrote to tell me that what I was describing was not exponential, but was actually polynomial.

They are quite correct.   I had mistakenly used “exponential” in the sense of “rapidly increasing”, which is a valid usage, but not too helpful in discussing algorithms.

To be clear, for a variable x, and a constant c,

x^c is polynomial

c^x is exponential.

This is confused a little by the use of n for the variable (as in the number of elements), as n is usually constant.

1. That’s not quite it either.

If c is not constrained to be an integer x^c is refered to more properly as a power function. If c is an integer and you want to stress that it’s only one term you can refer to it as a monomial.

Comment by Soylent — April 23, 2008 @ 1:43 pm

2. n is not used for a constant; rather for working with the set of positive integers.

Comment by me — May 28, 2008 @ 7:25 am