The alias method is a method for randomly selecting an element from a set in wich each element has an arbitrary probability of being selected.
The usual way this task is performed is by doing a binary search on the accumulated distribution array, this requires O(log n) comparisions, which for most cases is acceptable.
But for big sets (with approximately a million elements) and large number of choices (O(n log(n)) choices) the alias method is vastly supperior.