Space requirements in the FKS scheme: A Loose Bound =================================================== The important thing to realize is that the space is measured in terms of "cells" of size log M, the space required to store an element of M. Claim: The FKS scheme uses at most O(S) cells. Proof. Here is the breakdown --- Space for the first level table N: N = S cells. Space for the next level tables: \sum (N_i choose 2) \leq 3N = 3S. Number of Hash functions: at most N+1 = S+1 Each takes at most 2(log M) bits, and hence at most 2 cells. Total space = 2(S+1) Total number of cells = 6S + 2. QED.