[MarcusBrutus]

the tilde notation is used for functions, e.g. you can say f(n) is ~g(n) and in that context has a rigorous meaning (limit of f(n)/g(n) is 1 as n goes to positive infinity). I haven't seen it being used with orders of growth notations (O, Θ or Ω) and my guess is that's ~O(1) is undefined or somebody's just taking liberties with the notations.