On Thu, Nov 04, 2010 at 10:00:40AM +0000, Dean Rasheed wrote:
> On 3 November 2010 09:24, Nicolas Barbier <nicolas(dot)barbier(at)gmail(dot)com> wrote:
> > 2010/11/2 Kenneth Marshall <ktm(at)rice(dot)edu>:
> >> Given that our hash implimentation mixes the input data well (It does.
> >> I tested it.) then a simple rotate-and-xor method is all that should
> >> be needed to maintain all of the needed information. The original
> >> hash function has done the heavy lifting in this case.
> > Even with the perfect hash function for the elements, certain
> > combinations of elements could still lead to massive collisions. E.g.,
> > if repeated values are typical in the input data we are talking about,
> > then the rotate-and-xor method would still lead to collisions between
> > any array of the same values of certain lengths, regardless of the
> > value. In Tom's implementation, as he mentioned before, those
> > problematical lengths would be multiples of 32 (e.g., an array of 32
> > 1s would collide with an array of 32 2s would collide with an array of
> > 32 3s, etc).
> Yeah, rotate-and-xor is a pretty weak hashing algorithm, since any
> array of 32 identical elements will hash to either 0 or -1. Similarly
> various permutations or multiples of that array length will cause it
> to perform badly.
> The multiply-by-m algorithm doesn't have that weakness, provided m is
> chosen carefully. There are a couple of qualities a good algorithm
> should possess:
> 1). The bits from the individual element hash values should be
> distributed evenly so that no 2 different hash values would result in
> the same contribution to the final value. This is easy to achieve -
> just make sure that m is odd.
> 2). The way that each element's hash value bits are distributed should
> be different from the way that every other element's hash value bits
> are distributed. m=31 achieves this pretty well, although there are
> plenty of other equally valid choices.
In my comment yesterday, I included a simple function that would
allow us to leverage our current hash functions mixing process to
scramble the bits effectively and retaining the maximum amount of
information in the hash.
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