Volunteers needed for cross solving study

[jazzthief81]

Dear friends,

Some of you may remember this post:
http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/430

In the study I did there I calculated some statistics for the
required number of moves for solving the cross of a fixed color.
Since most people always start with the same color, these figures
give us a good idea of what the target should be for speedcubing.

Lately there have been some discussions on whether being color
neutral is a big advantage for people who start with building the
cross. Of course, it's easy to find single cases where the white
cross can't be solved in under 8 moves but the yellow cross is
already solved. But that doesn't tell us a lot about whether color
neutrality is better compared to fixed color cross solving in the
long run.

That's why I'm currently redoing the same experiment for solving the
cross on _any_ face. The intermediate results can be seen here:
http://www.cubezone.be/colorneutrality.html

I've done about 18% of the all the cases at the moment, and this took
about 10 days. I plan to repeat this experiment for quarter turn
metric (this current calculations use face turn metric), and I think
it would also be interesting to investigate opposite cross solving
and see where it is placed against fixed color cross solving and
complete color neutral cross solving.

I'm very excited to know what the results will end up being, but I
don't feel like waiting for another 2-3 months. That's why I was
hoping that we could tackle this problem in SETI@home style and
distribute the work over various machines. I've made a small client
that is able to do generate all edge positions and solve them:
http://www.cubezone.be/colorneutralityathome.zip

Just download, extract, and launch run.bat and it will connect to a
server and retrieve a package from it. A package in this case
corresponds to all positions that have the same pattern of flipped/
unflipped edges. Once it has finshed processing a package, it will
send the results to the server and retrieve a new one.

If you want to contribute to this study, feel free to download the
client application and process some packages. It will take up
virtually no memory or network bandwidth, but it will keep your
processor busy all the time.

Thanks for your help.

Kind regards,
Lars

 

[Stefan]

Very nice, I'm looking forward to those results as well. Especially quarter turn metric.

Of course, it's easy to find single cases where the white cross can't be solved in under 8 moves but the yellow cross is
already solved.

Are you sure? Can you show one?

 

[Mik]

The .bat file looks safe, opened it up in textedit and there's nothing bad.
Can't run those on Mac's though...

 

[Bryan]

Does anyone know of a simple webpage where I could enter in the 4 cross pieces and have it tell me the optimal algorithm? I always have problems recognizing the 7 moves, and if I could have something that would always show me the answer, I could learn that way (as opposed to looking at three or four examples from a webpage).

I'm guessing CubeExplorer has this feature, but I wanted something a little more lightweight that I could access from work easily.

 

[FU]

Does anyone know of a simple webpage where I could enter in the 4 cross pieces and have it tell me the optimal algorithm? I always have problems recognizing the 7 moves, and if I could have something that would always show me the answer, I could learn that way (as opposed to looking at three or four examples from a webpage).

I'm guessing CubeExplorer has this feature, but I wanted something a little more lightweight that I could access from work easily.

Johannes' optimal cross solver. Do a search on the forum for it.

 

[jazzthief81]

The .bat file looks safe, opened it up in textedit and there's nothing bad.
Can't run those on Mac's though...

You can, Mik. You can open a terminal and type:
sh run.bat

or you can rename it to run.sh and run it straight from the Finder. I will add a shell script to the zip file for convience.

 

[Pedro]

I'm helping, Lars

so...when I'm "tired" of doing it, I just close the client?
or do I have to wait until a package is finished?

 

[jazzthief81]

I'm helping, Lars

so...when I'm "tired" of doing it, I just close the client?
or do I have to wait until a package is finished?

Yes, Pedro.

You can just close it down at any time. At the moment the work it has done on the current package will be lost, but that's not a big deal. If a downloaded package is not being processed within one day, it will get sent to another person.

 

[Stefan]

It will take up virtually no memory

That might explain why it takes so long. Are you actually solving each case instead of looking up the distance for each cross?

And wow, I just saw there were already 16 cases found which take 8 moves! I was thinking about betting there won't be any.

 

[jazzthief81]

It will take up virtually no memory

That might explain why it takes so long. Are you actually solving each case instead of looking up the distance for each cross?

No it looks up the the 6 possible crosses in a precalculated table and takes the minimal distance.

 

[Stefan]

Alright... sorry about that. I very much overestimated the memory the tables would take.

 

[KoenHeltzel]

Hey Lars,

Interesting study.. i'm in.

Greets, Koen

 

[jazzthief81]

Alright... sorry about that. I very much overestimated the memory the tables would take.

Yeah, it's just 6 times 190080 entries.

Where the applications spends its time is generating a cube from the edge case with a given number and then calculating 6 indices from that.

 

[Johannes91]

Do you reduce symmetric positions? If not, that would be one way to speed it up.

And wow, I just saw there were already 16 cases found which take 8 moves! I was thinking about betting there won't be any.

And here's one where each 2x2x2 blocks requires 8 moves: B' F R D' U B2 R2 B' L' R D F2 U L2 R2 D' R2 D'.

Now, who wants to do a complete calculation like this for 2x2x2 block?

 

[Stefan]

Ok, two suggestions to maybe make it faster, although I know that'd might be a lot harder to implement. So I don't suggest to do these, I'd just like to throw them out as ideas.

1) Orientation as inside loop. Then from one cube to the next, you'd just have to flip edges, which probably means only flipping some bits in your six indices, right? And if you used Gray code (for the "first" eleven bits), that would even be just two bits (one from the Gray code, plus the remaining twelfth bit), so very little change between two cubes.

2) Symmetries... i.e. somewhat only do about 1/48 (or 1/96 thanks to inverses?) of all cases. Not sure how to do this, though. Scares me.

 

[AvGalen]

Do you reduce symmetric positions? If not, that would be one way to speed it up.

And wow, I just saw there were already 16 cases found which take 8 moves! I was thinking about betting there won't be any.

And here's one where each 2x2x2 blocks requires 8 moves: B' F R D' U B2 R2 B' L' R D F2 U L2 R2 D' R2 D'.

Now, who wants to do a complete calculation like this for 2x2x2 block?

That scramble should be considered "illegal" for FMC

The client is running on my pc now. Too bad it requires a "cmd" and a "java" window to stay open.

I hope you will do the same for a 2x2x2 block and after that for a cross OR 2x2x2 block. Maybe a scramble will come up that requires 8 moves for both cross AND 2x2x2

 

[Stefan]

I hope you will do the same for a 2x2x2 block

That'd be *a lot* harder (and this is a huge understatement).

 

[Johannes91]

I hope you will do the same for a 2x2x2 block

That'd be *a lot* harder (and this is a huge understatement).

Indeed...

Maybe a scramble will come up that requires 8 moves for both cross AND 2x2x2

Once this calculation is done, it shouldn't be too hard to go through all the 8-movers and see if it's possible to place the corners in a way that requires 8 moves for 2x2x2 blocks, too. But I can't believe such a position exists.

 

[jazzthief81]

Ok, two suggestions to maybe make it faster, although I know that'd might be a lot harder to implement. So I don't suggest to do these, I'd just like to throw them out as ideas.

1) Orientation as inside loop. Then from one cube to the next, you'd just have to flip edges, which probably means only flipping some bits, right? And if you used Gray code (for the "first" eleven bits), that would even be just two bits (one from the Gray code, one from the remaining twelfth bit), so very little change between two cubes.

Indeed, this would speed it up. The good thing about putting the orientation as the outside loop, is that we get all the statistics grouped by orientation pattern for free. The correlation with the flip of the edges is quite interesting. It also gives us a nice and workable amount of packages to distribute.

2) Symmetries... i.e. somewhat only do about 1/48 (or 1/96 thanks to inverses?) of all cases. Not sure how to do this, though. Scares me.

Absolutely true, but it scares me too and it would make things a lot more complicated to implement. Moreover, it would be hard to tell afterwards whether we didn't skip any positions. Doing it this way, if we can recognize the cube symmetries from the results at least we have some proof that it actually checked all edge cases.

 

[fw]

If you would also add a text-based version (no GUI), I could run this in background on some servers..