[Help Thread] FMC Discussion

[blah]

Hey guys. Is it humanly possible to utilize a variant of the two-phase algorithm (used from Cube Explorer) during FMC. I'm thinking of this, and I'm currently looking for papers about the two-phase, but I can only find descriptions, not any papers.

Human Thistlethwaite.

 

[blah]

All 6-move edge5-cycles:

...

I looked deeper into them, and found that there are 3 types of "algorithms":

1. S F S' F'
2. F S F' S'
3. Conjugated S F S' F'
(S = quarter slice turn; F = quarter face turn, which obviously cannot be parallel to S)

The first two are pretty straightforward. I found the third one pretty interesting, I'll describe it with an example:

U D' R U' D B' is a Type 1 "algorithm". Using D as a setup move, we get D (U D' R U' D B') D' = U R U' D B' D', which is a Type 3 "algorithm". That's it, that's what all the Type 3 algs are.

I doubt knowing 5-cycles are gonna be very useful in FMC, but at least knowing all the 6-movers can turn a nasty situation into a very nice one if you're lucky enough

I've found a use for these I don't have hard stats yet, but I believe it's not uncommon to have a Roux ending with 2 edges flipped and 3 edges to be cycled. Here's the most efficient solution I can't think of: Use a 5-cycle (insertion) to solve 2 of the 5 edges, and then a 3-cycle (insertion) to solve the remaining 3. I think with some cancellations it's possible to solve the remaining 5 edges in 10 moves or fewer. Is this a good idea?

 

[Zeroknight]

Human Thistlethwaite.

Right, I always remember I have to look it up, but never do. I hope I get it done this time, thanks.

 

[Johannes91]

I'm currently looking for papers about the two-phase, but I can only find descriptions, not any papers.

What kind of papers do you need and what for?

 

[Zeroknight]

'Paper(s)' is computer-nerd jargon for something written about something (but I mean, you probably know that, you have php in your sig ). So in this case, I'm looking for something (like an article, for example) about the two-phase algorithm. Why, what did you think I meant?

 

[blah]

'Paper(s)' is computer-nerd jargon for something written about something (but I mean, you probably know that, you have php in your sig ). So in this case, I'm looking for something (like an article, for example) about the two-phase algorithm. Why, what did you think I meant?

So you mean documentation?

@Johannes: That's PHP? I've been wondering for a while now. Looks nothing like the noob PHP I've learned

 

[fanwuq]

'Paper(s)' is computer-nerd jargon for something written about something (but I mean, you probably know that, you have php in your sig ). So in this case, I'm looking for something (like an article, for example) about the two-phase algorithm. Why, what did you think I meant?

My definition is either an essay I write for school or something published in a scientific journal.

You can probably find some info on the cubeexplorer site.

Why is everyone so focused on 3x3 FMC? What about 4x4 FMC?

 

[Zeroknight]

@Johannes: That's PHP? I've been wondering for a while now. Looks nothing like the noob PHP I've learned

Well, it was a guesstimation. I know that the php concatenator is a period, and variable are declared with $. It might also throw you off because it's output (I guess?) is in another language.

You can probably find some info on the cubeexplorer site.

I checked, I found the under 26 moves paper, but none specifically, in-depth for the TP.

Thanks though guys.

 

[Johannes91]

'Paper(s)' is computer-nerd jargon for something written about something (but I mean, you probably know that, you have php in your sig ). So in this case, I'm looking for something (like an article, for example) about the two-phase algorithm. Why, what did you think I meant?

I thought you meant academic publications specifically. That's the meaning of the word I'm used to. Maybe not exactly what you're looking for, but here's a lot of information about it and cube theory in general: http://cubezzz.homelinux.org/drupal/.

It's Perl btw (a JAPH).

 

[blah]

'Paper(s)' is computer-nerd jargon for something written about something (but I mean, you probably know that, you have php in your sig ).

Yes I know. It's Perl btw (a JAPH).

Pardon me for being nosy, but may I know what that piece of code does?

Edit: Oh. Just read your edit.

 

[Cride5]

A situation I often end up with in the end game is an 2 edge swap. It kinda stuffs up my solves because I'm fine with 3-edge/corner cycles, but swaps are just a nightmare! Usually I do a J perm (10 moves min), but according to Cube Explorer it can be done in 8-moves min. Here are all optimal edge swaps:

(two oriented edges to swap adjacent on same face - UF/UR)

U R U R' U R U2 R' (8f*)
U R2 U R2 U R2 U2 R2 (8f*)
U R' U R U R' U2 R (8f*)
U L U2 L' U L U L' (8f*)
U L2 U2 L2 U L2 U L2 (8f*)
U L' U2 L U L' U L (8f*)
U B U B' U2 B U B' (8f*)
U B2 U B2 U2 B2 U B2 (8f*)
U B' U B U2 B' U B (8f*)
U' F U' F' U' F U2 F' (8f*)
U' F2 U' F2 U' F2 U2 F2 (8f*)
U' F' U' F U' F' U2 F (8f*)
U' L U' L' U2 L U' L' (8f*)
U' L2 U' L2 U2 L2 U' L2 (8f*)
U' L' U' L U2 L' U' L (8f*)
U' B U2 B' U' B U' B' (8f*)
U' B2 U2 B2 U' B2 U' B2 (8f*)
U' B' U2 B U' B' U' B (8f*)
R U2 R' U' R U' R' U' (8f*)
R2 U2 R2 U' R2 U' R2 U' (8f*)
R' U2 R U' R' U' R U' (8f*)
F U2 F' U F U F' U (8f*)
F2 U2 F2 U F2 U F2 U (8f*)
F' U2 F U F' U F U (8f*)
L U L' U2 L U L' U (8f*)
L U' L' U' L U2 L' U' (8f*)
L2 U L2 U2 L2 U L2 U (8f*)
L2 U' L2 U' L2 U2 L2 U' (8f*)
L' U L U2 L' U L U (8f*)
L' U' L U' L' U2 L U' (8f*)
B U B' U B U2 B' U (8f*)
B U' B' U2 B U' B' U' (8f*)
B2 U B2 U B2 U2 B2 U (8f*)
B2 U' B2 U2 B2 U' B2 U' (8f*)
B' U B U B' U2 B U (8f*)
B' U' B U2 B' U' B U' (8f*)

(two oriented edges to swap opposite on same face - UF/UB)

R F U2 L F' L' U2 R' F' (9f*)
R B' R' U2 L' B' L U2 B (9f*)
R' F R U2 L F L' U2 F' (9f*)
R' B' U2 L' B L U2 R B (9f*)
F U2 F U2 F U2 F U2 F (9f*)
F U2 L F' L' U2 R' F' R (9f*)
F R U2 L F L' U2 F' R' (9f*)
F' U2 R' F R U2 L F L' (9f*)
F' U2 F' U2 F' U2 F' U2 F' (9f*)
F' L' U2 R' F' R U2 F L (9f*)
L F' L' U2 R' F' R U2 F (9f*)
L B U2 R B' R' U2 L' B' (9f*)
L' F' U2 R' F R U2 L F (9f*)
L' B L U2 R B R' U2 B' (9f*)
B U2 R B' R' U2 L' B' L (9f*)
B U2 B U2 B U2 B U2 B (9f*)
B L U2 R B R' U2 B' L' (9f*)
B' U2 L' B L U2 R B R' (9f*)
B' U2 B' U2 B' U2 B' U2 B' (9f*)
B' R' U2 L' B' L U2 B R (9f*)

(two edges diagonally opposite through cube UF/DB)

U L2 D' L2 U' F2 D' F2 D (9f*)
U B2 U' B2 U' B2 U' B2 U (9f*)
U B2 U' B2 D' R2 U' R2 D (9f*)
U' R2 D R2 U F2 D F2 D' (9f*)
U' B2 U B2 U B2 U B2 U' (9f*)
U' B2 U B2 D L2 U L2 D' (9f*)
F R2 B' R2 F' U2 B' U2 B (9f*)
F D2 F' D2 F' D2 F' D2 F (9f*)
F D2 F' D2 B' L2 F' L2 B (9f*)
F' D2 F D2 F D2 F D2 F' (9f*)
F' D2 F D2 B R2 F R2 B' (9f*)
F' L2 B L2 F U2 B U2 B' (9f*)
D F2 D' F2 U' R2 D' R2 U (9f*)
D F2 D' F2 D' F2 D' F2 D (9f*)
D L2 U' L2 D' B2 U' B2 U (9f*)
D' R2 U R2 D B2 U B2 U' (9f*)
D' F2 D F2 U L2 D L2 U' (9f*)
D' F2 D F2 D F2 D F2 D' (9f*)
B U2 B' U2 F' L2 B' L2 F (9f*)
B U2 B' U2 B' U2 B' U2 B (9f*)
B R2 F' R2 B' D2 F' D2 F (9f*)
B' U2 B U2 F R2 B R2 F' (9f*)
B' U2 B U2 B U2 B U2 B' (9f*)
B' L2 F L2 B D2 F D2 F' (9f*)

Some of them are also corner 3-cycles which is nice because it enables you to solve the corners at the same time as doing an edge swap

 

[fanwuq]

You will have to correct the edge permutation before you get to that point.
http://www.ryanheise.com/cube/edges_first.html

Edit: Your 8 movers are just Sunes and that all oriented MGLS case.

 

[AvGalen]

Hey guys. Is it humanly possible to utilize a variant of the two-phase algorithm (used from Cube Explorer) during FMC. I'm thinking of this, and I'm currently looking for papers about the two-phase, but I can only find descriptions, not any papers.

Short answer: no
Longer answer: That depends on the variant
Full answer: 1 step is 12 moves, the other step is 18 moves. Even with the reduced amount of turns (not all 18 moves are allowed always) people just cannot look ahead that far. And if you want to use the extra optimisation step (mixing the 2 phases for even shorter solutions) that is just not humanly doable

You should try to do 1 cube like that and find a (near) optimal solution for both steps. Good luck

 

[Johannes91]

Hey guys. Is it humanly possible to utilize a variant of the two-phase algorithm (used from Cube Explorer) during FMC.

Full answer: 1 step is 12 moves, the other step is 18 moves. Even with the reduced amount of turns (not all 18 moves are allowed always) people just cannot look ahead that far.

The second step isn't hard unless you want to be optimal every time. There's no need to look ahead much.

The main problem is the first step. How much doing it in two substeps would lose or how feasible it'd be to do at once are interesting questions. I don't think anyone has really looked into it.

Those numbers are upper bounds, btw, so it's like saying that cross and 2x2x2 block are 8 moves.

And if you want to use the extra optimisation step (mixing the 2 phases for even shorter solutions) that is just not humanly doable

They aren't mixed. It's simply that many different solutions for the first step, including sub-optimal ones, are tried. And that's exactly what humans are already doing in FMC.

 

[blah]

@Cride5: I don't know... 8 moves seems a little too much just to swap 2 edges. I'd rather go back into my solution and somehow add a quarter turn somewhere to make edge permutation parity even (I don't know if this is even possible, never tried it before ).

 

[Cride5]

You will have to correct the edge permutation before you get to that point.
http://www.ryanheise.com/cube/edges_first.html

Edit: Your 8 movers are just Sunes and that all oriented MGLS case.

Soz, I was in quite a hurry to get out the door when I generated them. Never had a chance to properly analyse them. I was hoping to find some elementary two-edge, two-corner swap operation in 8 moves, but it appears that collection of 8-movers permutes four corners in all cases. Probably not so useful for FM

For what its worth, these are the ones which operate on the LL corners only (part of ZBLL):
U R U R' U R U2 R' -- sune, URF oriented, anti-clockwise corner rotate
B U B' U B U2 B' U -- sune, URF oriented, anti-clockwise corner rotate
U L' U2 L U L' U L -- sune, UFL oriented, anti-clockwise corner rotate
F' U2 F U F' U F U -- sune, UFL oriented, anti-clockwise corner rotate
L' U' L U' L' U2 L U' -- anti sune, URF oriented, clockwise corner rotation
U' F' U' F U' F' U2 F -- anti sune, URF oriented, clockwise corner rotation
U' B U2 B' U' B U' B' -- anti sune, UBR oriented, clockwise corner rotation
R U2 R' U' R U' R' U' -- anti sune, UBR oriented, clockwise corner rotation

Most of the rest permute at least one corner on the bottom layer (like MGLS) and a few permute two bottom layer corners.

@Cride5: I don't know... 8 moves seems a little too much just to swap 2 edges. I'd rather go back into my solution and somehow add a quarter turn somewhere to make edge permutation parity even (I don't know if this is even possible, never tried it before ).

Hmm, yea ... edge swap permutation is one of those nightmare scenarios to avoid at all costs. 8 moves was the minimum Cube Explorer found when ignoring corners. This is a scenario which often messes up my end game! Guess its back to the drawing board for me

 

[AvGalen]

Hey guys. Is it humanly possible to utilize a variant of the two-phase algorithm (used from Cube Explorer) during FMC.

Full answer: 1 step is 12 moves, the other step is 18 moves. Even with the reduced amount of turns (not all 18 moves are allowed always) people just cannot look ahead that far.

The second step isn't hard unless you want to be optimal every time. There's no need to look ahead much.

The main problem is the first step. How much doing it in two substeps would lose or how feasible it'd be to do at once are interesting questions. I don't think anyone has really looked into it.

Those numbers are upper bounds, btw, so it's like saying that cross and 2x2x2 block are 8 moves.

And if you want to use the extra optimisation step (mixing the 2 phases for even shorter solutions) that is just not humanly doable

They aren't mixed. It's simply that many different solutions for the first step, including sub-optimal ones, are tried. And that's exactly what humans are already doing in FMC.

I would really like to see a human do step 1 and step 2 optimally and then doing ever more suboptimal variations to get even shorter (more optimal ) step 2's. Seeing a block or cross in 8 moves is already very hard, but is doable because there is so much freedom.

Is there any study that shows the distribution of the amount of moves for step 1 and for step 2?

 

[blah]

Is there any study that shows the distribution of the amount of moves for step 1 and for step 2?

I don't really know much about the original Thistlethwaite algorithm so I might be wrong, but if I recall correctly, I thought he had lookup tables for each step of his algorithm? Wouldn't an analysis of all the sequences in the tables for steps 1 and 2 suffice to show "the distribution of the amount of moves"?

I'm not even sure whether or not what I just said made any sense At least it makes sense to me with whatever limited knowledge of the Thistlethwaite algorithm I have. Please point me to a correct direction in case that doesn't make sense

 

[cuBerBruce]

Is there any study that shows the distribution of the amount of moves for step 1 and for step 2?

I think this is what you're asking for.

http://www.math.rwth-aachen.de/~Mar...s/michael_reid__two_stage_filtration_(2).html

http://www.math.rwth-aachen.de/~Mar...T._Winter__Re___two_stage_filtration_(2).html

 

[Zeroknight]

Thanks guys for the help, and I love Cube Theory (which I still need to go back and finish)