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From: bn77 on 25 Mar 2010 07:11
Hi,

I'm trying to write a program in mathematica that compares roughly (15!)^2 / 2 pairs of permutations of length 15. Can mathematica do this in a reasonable time? Any experience of this sort?

TIA,
bn77

From: Sjoerd C. de Vries on 26 Mar 2010 06:35
I don't think any PC could do this in reasonable time.

Just assume that every comparison would take one clock cycle on a 4
GHz PC. The whole process would then take more than 7 million years.

Cheers -- Sjoerd

On Mar 25, 1:11 pm, bn77 <nayantara.bhatna...(a)gmail.com> wrote:
> Hi,
>
> I'm trying to write a program in mathematica that compares roughly (15!)^2 / 2 pairs of permutations of length 15. Can mathematica do this in a reasonable time? Any experience of this sort?
>
> TIA,
> bn77


From: Bill Rowe on 26 Mar 2010 06:36
On 3/25/10 at 6:11 AM, nayantara.bhatnagar(a)gmail.com (bn77) wrote:

>I'm trying to write a program in mathematica that compares roughly
>(15!)^2 / 2 pairs of permutations of length 15. Can mathematica do
>this in a reasonable time? Any experience of this sort?

Forget execution time for a moment. Have you considered how much
memory would be needed to hold these pairs?

In[1]:= Log[10, (15!)^2] // N

Out[1]= 24.233

I am absolutely certain you don't have access to a machine with
any where near 10^25 bytes.

You very much need to consider a different approach to whatever
problem you are trying to solve.


From: Leonid Shifrin on 26 Mar 2010 06:38
Hi,

Looks like too large of a number to me, and not just for Mathematica, but
pretty much any language.

In[2]:= (15!)^2

Out[2]= 1710012252724199424000000

A simple estimate for a single 3Ghz machine gives about 10^11 hours to
perform (15!)^2 operations, assuming that we have 1 operation per clock
cycle. Looks like you have to greatly reduce your search space. In addition
to that, for problems of this type I'd consider using CUDA or something
similar to parallelize your problem.

Regards,
Leonid





On Thu, Mar 25, 2010 at 4:11 AM, bn77 <nayantara.bhatnagar(a)gmail.com> wrote:

> Hi,
>
> I'm trying to write a program in mathematica that compares roughly (15!)^2
> / 2 pairs of permutations of length 15. Can mathematica do this in a
> reasonable time? Any experience of this sort?
>
> TIA,
> bn77
>
>


From: Nicola Mingotti on 26 Mar 2010 06:35
On 2010-03-25 12:11:52 +0100, bn77 said:

> Hi,
>
> I'm trying to write a program in mathematica that compares roughly
> (15!)^2 / 2 pairs of permutations of length 15. Can mathematica do this
> in a reasonable time? Any experience of this sort?
>
> TIA,
> bn77

The number of permutations is then :
N[((15!)^2)/2] => 8.55006*10^23

Supposing you can compare 10^9 objects per second
you would need 10^4 seconds that is 3.171 milion years
according to Wolfram Alpha conversion.

So, no ! If you really need to cycle through all these objects
it's impossible. Brute force here fails, you need to find a smarter
way to solve it.

bye

Nicola.

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