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MathGroup Archive 2012

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Re: How best to implement a hash table in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125048] Re: How best to implement a hash table in Mathematica
  • From: David Bailey <dave at removedbailey.co.uk>
  • Date: Sun, 19 Feb 2012 06:33:14 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jho21j$5sb$1@smc.vnet.net>

On 18/02/2012 11:28, Joseph Gwinn wrote:
> I have an application that resembles dictionary lookup, with significant
> rates of collision.
>
> The current approach is to initialize the hash table, a 10^4 element
> list of empty sublists, and then build the table by inserting document
> object id numbers into the correct sublists as indexed by some important
> property of the object.  The choice of property varies with application.
> The property may be quantized geographic location, or some attribute of
> the object itself.
>
> When done building the hash table, query consists of reading the sublist
> using an index derived in the same way as for the original building of
> the list.  Each sublist may have many entries, and the entries need not
> be numbers.
>
> Anyway, I have a workable approach using
>
> HashList[[index]]=
> Union[Flatten[Join[HashList[[index]],{new object ID}]]]]
>
> as the core update function, but I'm wondering how well this will scale
> to say 10^6 sublists (which may be needed to keep the collisions under
> control with large datasets), and of course if there is a better way in
> Mathematica.
>
> I did look at SparseArrays, but they don't support elements that are
> sublists.
>
> Although this hash table is one dimensional, I have uses for 2D and
> maybe 3D tables, which are very common when one is hashing physical
> location.
>
> Thanks in advance,
>
> Joe Gwinn
>
Before constructing a hash table (other than for pedagogical reasons), I 
would try the built in mechanisms of Mathematica. For example, here is a 
trivial loop which creates a 'hash table' called hashtable, with values 
f[key]:

kk=1;
While[kk < 100000,
hashtable[kk]=f[kk];
kk++;
];

Of course, in this example the keys to the table are just the integers, 
but the built-in mechanism will work with keys of any structure.

When a function is defined in this way as lots of individual values, 
Mathematica uses techniques (probably hash) to access the values. Try it 
and see how efficient it is!

David Bailey
http://www.dbaileyconsultancy.co.uk




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