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WANTED: New Dedge Flip Algorithm!

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Dec 11, 2009
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Is it just me, or do all "pure" OLL dedge flip parity algs for 4x4x4 stink!

Why do these algs have to be pure, or so careful about changing LL when it is easy to discover the parity at an earlier point in the solve?

I want to fix this parity flip as soon as I find it, but these "pure" or "OLL pure" appear to be wasting moves by pointlessly putting pieces into positions that weren't solved yet anyway.

Can anybody PLEASE come up with an all New 4x4x4 dedge flip algorithm that is NOT pure, and can take full advantage of a not yet solved F2L pair and a free LL?

reThinker
 

Toad

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Why not just wait until you get to LL to do it...

It'll waste more moves having to setup for this alg so as not to ruin the bits of the cube that are already solved...?
 
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Why not just wait until you get to LL to do it...

It'll waste more moves having to setup for this alg so as not to ruin the bits of the cube that are already solved...?
You can see whether or not you need to execute the OLL parity quite easily with only one F2L pair left to do.
 

Lucas Garron

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I'm not sure I agree with your title, but:
http://www.speedsolving.com/forum/showpost.php?p=239386&postcount=5

r' U R U (r' U2)3 r2 U R' U' r2 U' R' U r'

Can anybody PLEASE come up with an all New 4x4x4 dedge flip algorithm that is NOT pure, and can take full advantage of a not yet solved F2L pair and a free LL?
Bolding doesn't really help. ;)

Anyhow, this doesn't look much easier (read: I don't think algs will be much shorter) than a regular ALL parity, and I find your request description a bit arbitrary.

But I do wonder what is "the" shortest algorithm that gets each orbit of 4x4x4 parity to a solvable 3x3x3 as fast as possible.
 
Last edited:

Christopher Mowla

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Your desire for such an algorithm cannot be satisfied. As randomtoad said, it will require more moves than the best odd parity algorithms that exist already. Your best bet is to just do double layer turns with one of the pure algorithms (like everyone already does).

The ideal algorithm, which you are interested in, can be derived from an pure “edge flip” algorithm in which its ending moves are only outer-layer turns, there by making it possible to omit those last moves so that you are not doing worthless 3X3X3 restoration (as long as those moves restore only the last layer and maybe one F2L slot, as you have requested).

There is no "dedge flip" algorithm that exists (which is shorter in length than the pure edge flip algorithms) that satisfies this constraint, nor will there ever be.

Proof:
There are two main reasons for this:
[1] "Edge flip" algorithms', or even just every pure odd parity algorithm’s, main goal is to preserve the centers: if they don’t preserve the centers, then you might as well use the Cage Method (which as you know is not going to give you a world record: commutators are an inefficient way to solve the centers).
[2] The wing edges need to be separated in the beginning of the algorithm and subsequently at the end of the algorithm (which is slice turns, not outer-layer turns).

Unlike all other forms of odd parity restricted to the LL, the "one edge flip" is the case which requires the most moves (or at least it is safe to say that, no other form of odd parity will actually require more than the least moves that the one-edge flip can be done in) because the two wing edges are initially in the same composite edge.

The "r2 B2" and "B2 r2" that you see at the beginning and end of common algorithms is to bring the initially front-right wing edge to the back-left, so that the front-left and back-left are directly across from each other (or vice versa, depending on which mirror you do). (Note: there are other ways to move two winged edges besides r2 B2/l2 B2, which are originally in the same composite edge, opposite to one another, in 4 block quarter turn moves, but this is the only way to get them across from each other in 2 block half turn moves).

For example, the best opposite winged edge swap from my understanding (or its mirror) is:

l' U2 l' U2 F2 l' F2 r U2 r' U2 l2

Now, to make this a pure edge flip, it is going to cost us some more moves. We start off with adding "l2 B2" to the beginning and "B2 l2" to the end.

l2 B2
l' U2 l' U2 F2 l' F2 r U2 r' U2 l2
B2 l2

But, we have a problem: the top and bottom centers are discolored slightly.

To fix this problem, all you need to do is add 1 half turn slice in the beginning and the end:

l2 B2 l2
l' U2 l' U2 F2 l' F2 r U2 r' U2 l2
l2 B2 l2

As you probably can see, there are three block quarter turn moves which disappear due to move cancellations, and we are left with a 25 block quarter turn alg/15 block half turn alg:

l2 B2 l U2 l' U2 F2 l' F2 r U2 r' U2 B2 l2

Just as the "base" for the alg above was l' U2 l' U2 F2 l' F2 r U2 r' U2 l2, if you try, you will find that the base of r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2 is:

r2 B2 r2
r2 U2 l U2 r' U2 r U2 F2 r F2 l' r2
r2 B2 r2

With all of that said, I just wanted to show you that you must first separate the dedge pieces (some how) in order to swap them.

As you have seen in the two previous examples, if you separate wing edges at the beginning of an alg, then you’re going to have to reverse it at the end. You are not going to be able to do the reverse of the slice turns so that all which remains after it are outer layer turns (well, unless you add in a lot of outer layer turns at the end, then maybe you could do this—you can try it, but I will not waste my time).

In short, your fantasy algorithm does not exist. (Here I am assuming that you desire an algorithm which is shorter than a typical edge flip alg because I definitely can say that such an algorithm that you are requesting will definitely not be “prettier” than what you already have access to).

End of Proof

Just as there are rules in integration that cause an infinite number of integrals to not exist, so are there rules for the cube. But in Calculus, we have the alternative to integrate a function (whose anti-derivative cannot be expressed in terms of elementary functions) by expanding the function as an infinite power series and integrating it term-by-term. Similarly, this algorithm can be done by expanding (adding in a lot more outer-layer turns at the end or making the overall length of the algorithm longer), but it will not be pretty (if it can even be done at all). But whether talking about cubing or calculus, the alternative is not very beautiful.

As Lucas Garron mentioned, maybe what you are really hungry for is a pure edge flip algorithm that is the least number of moves. I am assuming he meant block quarter turn moves, because in block half turn moves, we already have the optimal algorithm (15).

For speedcubing purposes, these briefest pure “edge flip” algorithms (in block quarter turn moves) are most likely not going to be necessarily faster to perform than the current algorithms (I perform a few of mine around the same amount of time), even though they might be 5-6 block quarter turn moves less.

If you absolutely hate the “one edge flip”, then use K4 (as V-te said). To make sure you avoid it using that method, first do commutators to make all of the LL yellow. Then do 1 of the 2 possible odd parity algorithms (or their mirrors). Unfortunately, this process often makes the cuber to do more moves than necessary to complete the LL edges.

You might think that the pure "edge flip" algorithms stink, but if you knew how much they accomplish, even though they are bounded by a very large number of constraints (the shorter the algorithm, the more constraints the composer of the algorithm has to overcome), you would develop a hate for the odd number of slice turns you use to solve the centers at the beginning! The "parity errors" therefore can be renamed "human errors" because we do have control to prevent them (but of course for speedcubing, there is no way to detect it in during inspection time—unless you are amazing). Pure odd parity algorithms are our "spare tires", if you will, and there is no "spare tire" which we can put on our car faster than what we already have.
 
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Christopher Mowla

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Is that really a proof ?
deadalnix,
For an edge flip algorithm, the wing edges must be separated in the beginning because no matter how many outer-layer turns you perform prior to the separation, it will not get you anywhere.

With that said, you must bring back the wing edges some time later. If you don't do it at the end, but some time before that so that all that is left is outer-layer turns that restore the LL and maybe one F2L slot, then it is going to take you more outer-layer moves to compensate for the "early wing edge reunion" which should have occurred at the end (symmetrical).

And notice most of all that reThinking the Cube wanted an algorithm that didn't "stink". There is no way you can have one that fits into his description that isn't a whole lot worse than the briefest existent algorithms already.
 
Last edited:
Joined
Dec 11, 2009
Messages
294
Your desire for such an algorithm cannot be satisfied. As randomtoad said, it will require more moves than the best odd parity algorithms that exist already. Your best bet is to just do double layer turns with one of the pure algorithms (like everyone already does).
I really appreciate this expose, and am in agreement with your take on this parity problem, but we appear to have a different understanding as to what this "algorithm" is supposed to be able to do.

Maybe to clear this up, I should first state what this New dedge flip algorithm is NOT supposed to do. That way we can all be working together here.

1) This algorithm does NOT have to restore the flipped dedge to its original location. I know the edge pieces need to be swapped and then paired back to reform the dedge, but the permutation of this piece can be any dedge position on LL or the yet to be solved dedge for F2L pair. So any of these 5 possible spots to return the dedge to is fine. This allows for more flexibility to find better base edge exchange algorithms that can be used to make the actual dedge flip.

2) F2L is solved except for the last slot pair, and LL is open. This algorithm then does NOT have to worry about making changes (psuedo 3x3x3) to any of these 10 locations. This should again make it easier to do the flip algorithm since changes are not only allowed here, but also do not have to be restored back again later. Another aspect of this restriction removal is that there are 5 corner pieces that are happy with any orientation, permutation, or parity situation. This is a HUGE advantage in terms of finding good finger friendly algs, as now the single slice moves (i.e r,r',l,l',u,u') can sometimes be coupled with their respective face turns making for example, changing [r u r' u'] into [(Rr) (Uu) (Rr)' (Uu)'] without messing up anything important.

3) This algorithm does NOT even have to flip just one dedge, and in fact can flip any odd number of dedges (1,3,5). If it turns out that there is a shorter pure edge exchange that works on more pieces (not likely, but still possible) then the parity issue would still be solved. In other words, it makes no difference how many we "flip", just as long as it is an odd number of dedges that get the treatment.

4) This algorithm must NOT unpair any of the dedges, as this would obviously be counterproductive. (Stated for the record).

5) This algorithm must NOT mess up the centers. (again for the record).

Are we seeing eye to eye on this now?

The ideal algorithm, which you are interested in, can be derived from an pure “edge flip” algorithm in which its ending moves are only outer-layer turns, there by making it possible to omit those last moves so that you are not doing worthless 3X3X3 restoration (as long as those moves restore only the last layer and maybe one F2L slot, as you have requested).
You probably see now that it is possible to create a better "unpure" edge flip algorithm that would satisfy the much looser conditions of this problem.

There is no "dedge flip" algorithm that exists (which is shorter in length than the pure edge flip algorithms) that satisfies this constraint, nor will there ever be.
This "proof" has some solid logic to it, BUT there is NO constraint for using only "pure" edge flips, or on having to restore the dedge to its original location. I believe that both better single edge swap algs and better dedge parity flips based on them will be found.

Proof:
There are two main reasons for this:
[1] "Edge flip" algorithms', or even just every pure odd parity algorithm’s, main goal is to preserve the centers: if they don’t preserve the centers, then you might as well use the Cage Method (which as you know is not going to give you a world record: commutators are an inefficient way to solve the centers).
[2] The winged edges need to be separated in the beginning of the algorithm and subsequently at the end of the algorithm (which is slice turns, not outer-layer turns).

Unlike all other forms of odd parity restricted to the LL, the "one edge flip" is the case which requires the most moves (or at least, no other form of odd parity will actually require more than the least moves that the one-edge flip can be done in) because the two winged edges are initially in the same composite edge.

The "r2 B2" and "B2 r2" that you see at the beginning and end of common algorithms is to bring the initially front-right winged edge to the back-left, so that the front-left and back-left are directly across from each other (or vice versa, depending on which mirror you do). (Note: there are other ways to move two winged edges besides r2 B2/l2 B2, which are originally in the same composite edge, opposite to one another, in 4 block quarter turn moves, but this is the only way to get them across from each other in 2 block half turn moves).

For example, the best opposite winged edge swap from my understanding (or its mirror) is:

l' U2 l' U2 F2 l' F2 r U2 r' U2 l2

Now, to make this a pure edge flip, it is going to cost us some more moves. We start off with adding "l2 B2" to the beginning and "B2 l2" to the end.

l2 B2
l' U2 l' U2 F2 l' F2 r U2 r' U2 l2
B2 l2

But, we have a problem: the top and bottom centers are discolored slightly.

To fix this problem, all you need to do is add 1 half turn slice in the beginning and the end:

l2 B2 l2
l' U2 l' U2 F2 l' F2 r U2 r' U2 l2
l2 B2 l2

As you probably can see, there are three block quarter turn moves which disappear due to move cancellations, and we are left with a 25 block quarter turn alg/15 block half turn alg:

l2 B2 l U2 l' U2 F2 l' F2 r U2 r' U2 B2 l2

Just as the "base" for the alg above was l' U2 l' U2 F2 l' F2 r U2 r' U2 l2, if you try, you will find that the base of r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2 is:

r2 B2 r2
r2 U2 l U2 r' U2 r U2 F2 r F2 l' r2
r2 B2 r2
Very nice expo on the logic used to create these algs. I appreciated that!

As Lucas Garron mentioned, maybe what you are really hungry for is a pure edge flip algorithm that is the least number of moves. I am assuming he meant block quarter turn moves, because in block half turn moves, we already have the optimal algorithm (15).

For speedcubing purposes, these briefest pure “edge flip” algorithms (in block quarter turn moves) are most likely not going to be necessarily faster to perform than the current algorithms (I perform a few of mine around the same amount of time), even though they might be 1-2 block quarter turn moves less.
What I want is the dirtiest, nastiest, pure, or unpure, single "edge flip" you can come up with. As long as it satisfies the conditions above - I will be VERY happy. It will not be a problem at all for me to invent the cube rotations, inversions, conjugations, and cancellations to optimize from there.

reThinker
 
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