Asymptotic analysis is based on the idea that as the problem size grows, the complexity can be described as a simple proportionality to some known function. This idea is incorporated in the Big Oh notation for asymptotic performance.Definition: T(n) = O(f(n)) if and only if there are constants c 0 and n 0 0 0.he following functions are often encountered in computer science Big Oh analysis: 1  T(n) = O(1). 2  This is called constant growth. 3  T(n) does not grow at all as a function of n, it is a constant.