Asymptotic Notation Definition and Application

Big Omega

Definition: Big-Omega, commonly written as Ω, is an Asymptotic Notation for the best case, or a floor growth rate for a given function. It provides us with an asymptotic lower bound for the growth rate of runtime of an algorithm. Application: For some Real Constants. f(n) is >= c g(n)

Small o

Definition: Small-o, commonly written as o, is an Asymptotic Notation to denote the upper bound (that is not asymptotically tight) on the growth rate of runtime of an algorithm. Application: For all constants. f(n) is < c g(n)

Small Omega ω

Definition: Small-omega, commonly written as ω, is an Asymptotic Notation to denote the lower bound (that is not asymptotically tight) on the growth rate of runtime of an algorithm. Application: For all real constants. f(n) is > c g(n) greater.

Theta Θ

Definition: Theta, commonly written as Θ, is an Asymptotic Notation to denote the asymptotically tight bound on the growth rate of runtime of an algorithm. Application: Falls between two constants. c1 g(n) is < f(n) is < c2 g(n) for every input size n (n > n0).

Big O

Definition: asymptotic upper bound. if for some real constants c (c > 0) and n0, f(n) <= c g(n) Application: f(n) <= g(n) holds for SOME constant c > 0