Re: hashtext () and collisions

On 2007-04-11, "Leon Mergen" <leon(at)solatis(dot)com> wrote:
> Now, my question is: how big is the chance that a collision happens
> between hashes ? I noticed that the function only returns a 32 bit
> number, so I figure it must be at least once in the 4 billion values.

Assuming it's a uniform random hash, 32 bits long, then if you have
65536 values, you have a ~40% chance of at least one collision. Any
defects in the hash function only increase that probability.

This is a result of what's known as the "birthday paradox" (so-called
because in a group of 23 people, there is a better than even chance that
two of them share a birthday). The number of rows needed to have an
approximately even chance of at least one collision grows as the
_square root_ of the number of hash buckets; or to put it another way,
you always need _more than twice as many bits_ in your hash value than
you think you do. (e.g. using md5(), which is a 128-bit hash)

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Andrew, Supernews
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