So as far as I know the weakly universal hashing is defined as:for any $x, y \subset U, Pr(h(x) = h(y)) \le \frac{1}{m}$ where m is a smaller number than the cardinality of $U$, and h are chosen randomly from a set of all possible hash function $H$.I am just wondering if we choose the hash of an item randomly from the set $Z_m$, then the probability of having a hash collision is $\frac{1}{m}$ for x and y. So the weakly universal hashing is a quite strong requirement on how to choose hash function isn't it? Why?
Isn't weakly universal hashing even a stronger than truly random?
ds.algorithms;ds.data structures;hash function