Thank you!
I have resolved for up to "geng 11". It is the 12 that I need a solution. I
am aware how many graphs it generates.
I used multi-core manually, i.e., I launched multiple(24) geng program on a
24-core machine.
There is no doubt that geng is much faster than using sagemath's
nauty_geng(python). Thank you for the suggestion.
With 12, I can't write to a file, it is at least 1500G. I can write to a
file up to around 300G at most.
That is why I am thinking how to divide the output of "geng 12". So far,
I don't have any idea. Any suggestion?
On Friday, March 22, 2019 at 1:37:42 AM UTC-7, Jori Mäntysalo (TAU) wrote:
>
> OK, more explanation.
>
> * * *
>
> First I compare time for generating graphs in Nauty and in Sage. As plain
> graphs(n) uses nauty, I have test.sage containing
>
> print(sum(1 for _ in graphs(9)))
>
> It takes about 11½ seconds to run. I tested this with
>
> time ./sage test.sage
>
> Then,
>
> ./local/bin/geng 9 > /dev/null
>
> says "274668 graphs generated in 0.12 sec". So, if we just want to sample
> few graphs, we can get the speedup of ~50x. In other words, it is slow to
> convert data to Python internal format.
>
> OTOH number of many finite structures up to isomorphism grows very fast.
> So you can for example test some hypothesis to n=10 on a mobile phone,
> n=11 on a desktop computer and n=13 on a supercomputer. Same happens when
> you optimize code.
>
> * * *
>
> Next, does geng use multiple cpu cores? No. There is no difference between
>
> time taskset -c 1 ./local/bin/geng 9 > /dev/null
> time taskset -c 1-4 ./local/bin/geng 9 > /dev/null
>
> (You could also use "top" to see cpu usage.)
>
> * * *
>
> Now, how to use geng, make a sample, and then get them to Sage? First I
> generated all graphs (here to n=9 for speed):
>
> $ ./local/bin/geng 9 > g9
> >A ./local/bin/geng -d0D8 n=9 e=0-36
> >Z 274668 graphs generated in 0.12 sec
>
> OK, now I have a big list of strings:
>
> $ head -3 g9 ; tail -3 g9
> H??????
> H????A?
> H????B?
> H]~~~~~
> H^~~~~~
> H~~~~~~
>
> Every line is an encoded graph. I want to make a sample, lets say every
> 1000:th line. Every line is (HERE, not when n=12) 8 bytes long. So,
>
> $ i=0; while [[ i -lt 274668 ]]; do dd if=g9 bs=8 skip=$i count=1 >>
> g9sample 2> /dev/null; i=$((i+1000)); done
>
> will give you a file of 275 lines:
>
> $ wc -l g9sample
> 275 g9sample
>
> And now I did a test2.sage -file:
>
> with open('g9sample', 'r') as fp:
> c = 0
> n = 0
> for line in fp:
> g = Graph(line, format='graph6')
> n += 1
> if g.is_connected():
> c += 1
> print("About %s percent are connected" % round(100.0*c/n))
>
> and
>
> $ ./sage test2.sage
> About 95 percent are connected
>
> Of course there are many other ways for this. For example you could read
> the whole file with Python and just skip 99,9% of lines, or skip every
> line with propability of 0.999 etc. Hopefully you get the idea from this.
>
> --
> Jori Mäntysalo
>
> Tampereen yliopisto - Ihminen ratkaisee
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