- To measure the time complexity in absolute time unit has the following problems
- The time required for an algorithm depends on number of instructions executed, which is a complex polynomial.
- The execution time of an instruction depends on computer's power. Since, different computers take different amount of time for the same instruction.
- Different types of instructions take different amount of time on same computer.
- Complexity analysis technique abstracts away these machine dependent factors . In this approach, we assume all instruction takes constant amount of time for execution.
- Asymptotic bounds as polynomials are used as a measure of the estimation of the number of instructions to be executed by the algorithm . Three main types of asymptotic order notations are used in practice:
1.
- notation :
For a given function g(n), 
is defined as
In other words, a function 
is said to belong to 
, if there exists positive constants 
and 
such that
for sufficiently large value of n. For example, 
. This is because we can find constants
such that
, for all
.