Hash/permutation function for object ID creation

#1 07-29-2008, 04:20 AM

I need a system to generate a series of "semi-random-non-repeating"
32-bit object IDs. For this, I plan to create a sequence counter
(starting from 0), then feed the sequence number, s, to a permutation
function, F(s). And use F(s) as the generated object ID. F() needs to
have the following properties:

1. F(x) is semi-random so that if the ID is partitioned into any
number of "buckets" (by equal range, or MOD hashing), each bucket
has roughly same number of objects.
2. F() has an inverse F' s.t. F(F'(x)) = x
3. Both F() and F'() are computationally "inexpensive" to compute

I will appreciate any help or link for such algorithm. Thanks in
advance,

Bruza

#2 07-29-2008, 07:09 AM

On 29 Jul., 10:20, Bruza <benr...@gmail.com> wrote:
> I need a system to generate a series of "semi-random-non-repeating"
> 32-bit object IDs. For this, I plan to create a sequence counter
> (starting from 0), then feed the sequence number, s, to a permutation
> function, F(s). And use F(s) as the generated object ID. F() needs to
> have the following properties:
>
> 1. F(x) is semi-random so that if the ID is partitioned into any
> number of "buckets" (by equal range, or MOD hashing), each bucket
> has roughly same number of objects.
> 2. F() has an inverse F' s.t. F(F'(x)) = x
> 3. Both F() and F'() are computationally "inexpensive" to compute
Why not use the identity function? It is not semi-random at all, but
using mod-based hash bucket assignment should work perfectly well. I
think giving a good answer to your question requires information why
identity won't suffice.

#3 07-29-2008, 09:16 PM

On Jul 29, 4:20*am, Bruza <benr...@gmail.com> wrote:
> I need a system to generate a series of "semi-random-non-repeating"
> 32-bit object IDs. For this, I plan to create a sequence counter
> (starting from 0), then feed the sequence number, s, to a permutation
> function, F(s). And use F(s) as the generated object ID. F() needs to
> have the following properties:
>
> * 1. F(x) is semi-random so that if the ID is partitioned into any
> * * *number of "buckets" (by equal range, or MOD hashing), each bucket
> * * *has roughly same number of objects.
> * 2. F() has an inverse F' s.t. F(F'(x)) = x
> * 3. Both F() and F'() are computationally "inexpensive" to compute

When I have to do this sort of thing for a simple hash table or
something, I usually do something simple like:

hash = ID+SOME_CONSTANT
hash *= SOME_ODD_CONSTANT
hash ^= (hash>>16)
hash ^= (hash>>8)

each line is reversible in modular arithmetic (mod 2^x), so the whole
function is reversible.

If you need something stronger, you can divide the ID into two halves
(L,R), and with a good hash function H(), do:

L' = L XOR H(R)
R' = R XOR H(L')

hash = (L',R')

This is called a Feistel network (googlable), and again each step is
obviously reversible.

Cheers,

Matt

#4 07-29-2008, 09:51 PM

On Jul 29, 6:16 pm, matt.timmerm...@gmail.com wrote:
> On Jul 29, 4:20 am, Bruza <benr...@gmail.com> wrote:
>
> > I need a system to generate a series of "semi-random-non-repeating"
> > 32-bit object IDs. For this, I plan to create a sequence counter
> > (starting from 0), then feed the sequence number, s, to a permutation
> > function, F(s). And use F(s) as the generated object ID. F() needs to
> > have the following properties:
>
> > 1. F(x) is semi-random so that if the ID is partitioned into any
> > number of "buckets" (by equal range, or MOD hashing), each bucket
> > has roughly same number of objects.
> > 2. F() has an inverse F' s.t. F(F'(x)) = x
> > 3. Both F() and F'() are computationally "inexpensive" to compute
>
> When I have to do this sort of thing for a simple hash table or
> something, I usually do something simple like:
>
> hash = ID+SOME_CONSTANT
> hash *= SOME_ODD_CONSTANT
> hash ^= (hash>>16)
> hash ^= (hash>>8)
>
> each line is reversible in modular arithmetic (mod 2^x), so the whole
> function is reversible.
>
> If you need something stronger, you can divide the ID into two halves
> (L,R), and with a good hash function H(), do:
>
> L' = L XOR H(R)
> R' = R XOR H(L')
>
> hash = (L',R')
>
> This is called a Feistel network (googlable), and again each step is
> obviously reversible.
>
> Cheers,
>
> Matt

Matt,

Great! Feistel network seems to be what I want. Thanks for your help.

Bruza

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