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Summary



o notation
f(n) = o(g(n)), g(n) is an upper bound of f(n) that is not asymptotically tight



$\omega$ notation
f(n) = $\omega(g(n))$, g(n) is a lower bound of f(n) that is not asymptotically tight
Example: f(n) = 3$n^3$ + 4
  • f(n) = $\Theta(n^3)$
  • f(n) = O($n^3$) = O($n^4$) = ...
  • f(n) = $\Omega(n^3)$ = $\Omega(n^2)$ = $\Omega(n)$ = $\Omega(1)$
  • f(n) = o($n^4$) = o($n^5$) = ...
  • f(n) = $\omega(n^2)$ = $\omega(n)$ = $\omega(1)$


next up previous
Next: Some Useful Mathematical Tools Up: l1 Previous: Asymptotic Notation in Equations