Difference between revisions of "Domino Reduction"

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"Domino Reduction"
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{{Substep Infobox
This method is most commonly used for FMC solutions.  
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|name=Domino Reduction
Also implemented by Cube Explorer to perform Optimal solutions for scrambles.
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|image=DR.png
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|proposers=[[Morwen Thistlethwaite]]
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|year=1981
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|anames=DR, Domino Phase, H1 (Thistlethwaite), G1 (Kociemba), Phase 1 (Kociemba)
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|variants=[[Partial Domino Reduction]], [[Half Turn Reduction]]
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|subgroup=
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|moves=9.53 (optimal)
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|algs=0-2217 million (number of positions)
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|purpose=<sup></sup>
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* [[Computer Algorithm]]
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* [[Fewest Moves]]
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* [[Speedsolving]]
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|previous=[[Scrambled cube state]]
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|next=[[Domino cube state]]
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}}
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'''Domino Reduction''' or '''DR''' is a technique invented by [[Morwen Thistlethwaite]]. It is employed by [[:Category:Computer algorithms|computer algorithms]], [[Speedsolving|speedsolvers]] and [[FMC|fewest move solvers]] to bring the [[3x3x3 cube]] into a state similar to the [[Rubik's Domino]]. This is accomplished by [[CO|orienting all the corners]] and performing [[2-axis EO]], reducing the cube from <U,D,L2,R2,F2,B2> to <U,D,L2,R2,F2,B2>. [[God's number]] for DR is 12.
  
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== Computer algorithms ==
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Domino Reduction was initially invented to allow computer algorithms to solve the cube efficiently.
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The first computer algorithm to utilize Domino Reduction was [[Thistlethwaite's algorithm]] in 1981. Due to hardware limitations back then, Domino Reduction is performed in two steps. The algorithm firstly orients the edges and then proceeds to orient the corners and separate the E-layer edges in one step. Using this approach, Domino Reduction can be reached in a maximum of 20 moves. Using two more steps after Domino Reduction, this algorithm was able to solve a cube in a maximum of 52 moves [[HTM]].
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11 years later, in 1992, [[Herbert Kociemba]] invented [[Kociemba's Algorithm]]. It's main difference from [[Thistlethwaite's algorithm]] is that the first two steps and the last two steps are combined into one step each, solving the cube in two "phases". Because of this, it is also called the Two-Phase-Algorithm. It was possible to store all positions using the more advanced technology and various optimizations like symmetry reduction described on [http://kociemba.org/cube.htm Kociemba's website]. This algorithm was able to solve Domino Reduction optimally in at most 12 moves and the whole cube in 29 moves.
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== Speedsolving ==
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Although Domino Reduction is very rarely used in speedsolving, various methods have been invented to allow human solvers to reduce to a domino state quickly.
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The first one was [[Human Thistlethwaite]], an adapted version of [[Thistlethwaite's algorithm]] for humans, proposed by [[Ryan Heise]] in 2002. Most of the reduction steps are either done intuitively or using a small set of pre-made algorithms. Because of the amount of thinking required and the relatively bad ergonomics of the method, virtually no one uses [[Human Thistlethwaite]] as their main speedsolving method.
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An unrelated method, [[SSC|Shadowslice Snow Columns]], was invented in 2015 by [[Joseph Briggs]]. It starts with [[EOEdge]], where [[EO|edges are oriented]] and two E-slice edges are solved. The solver then proceeds by building a pseudo-pair and a pseudo-triplet and performing one of 23 algorithms. This solves the last two E-slice edges and orients the corners, effectively reducing the cube to a domino state with all E-slice edges solved. After this step, there are multiple ways to finish. The finish usually has pretty good ergonomics (R2, U, D and M moves) and makes the solve 40 to 50 moves STM long. SSC is a much more viable method for speedsolving than Human Thistlethwaite, although it's still rarely used because it drastically differs from mainstream speedsolving methods and since a good way to finish the cube after DR still needs to be found.
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Although Domino Reduction might be viable for speedsolving, it is still not developed enough and too different from other methods to be adapted by more people in the near future.
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== Fewest moves ==
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{{work}}
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== See also ==
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* [[Morwen Thistlethwaite]]
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* [[Corner Orientation]]
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* [[2-axis EO]]
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* [[Thistlethwaite's algorithm]]
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* [[Kociemba's Algorithm]]
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* [[FMC]]
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* [[Human Thistlethwaite]]
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* [[SSC]]
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* [[Half Turn Reduction]]
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== External links ==
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* [https://www.speedsolving.com/threads/a-domino-reduction-guide-for-fmc.74828/ A Domino Reduction Guide by Alexandros Fokianos and Tommaso Raposio]
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* [http://kociemba.org/cube.htm Kociemba's website, including his Two-Phase-Algorithm]
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* [http://kociemba.org/math/distribution.htm Kociemba's distribution of moves required for DR]
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* [https://www.jaapsch.net/puzzles/thistle.htm Jaap's page about Thistlethwaite's algorithm]
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[[Category:3x3x3 first substeps]]

Revision as of 10:37, 27 June 2020

Domino Reduction
DR.png
Information
Proposer(s): Morwen Thistlethwaite
Proposed: 1981
Alt Names: DR, Domino Phase, H1 (Thistlethwaite), G1 (Kociemba), Phase 1 (Kociemba)
Variants: Partial Domino Reduction, Half Turn Reduction
Subgroup:
No. Algs: 0-2217 million (number of positions)
Avg Moves: 9.53 (optimal)
Purpose(s):
Previous state: Scrambled cube state
Next state: Domino cube state

Scrambled cube state -> Domino Reduction step -> Domino cube state


The Domino Reduction step is the step between the Scrambled cube state and the Domino cube state.

Domino Reduction or DR is a technique invented by Morwen Thistlethwaite. It is employed by computer algorithms, speedsolvers and fewest move solvers to bring the 3x3x3 cube into a state similar to the Rubik's Domino. This is accomplished by orienting all the corners and performing 2-axis EO, reducing the cube from <U,D,L2,R2,F2,B2> to <U,D,L2,R2,F2,B2>. God's number for DR is 12.

Computer algorithms

Domino Reduction was initially invented to allow computer algorithms to solve the cube efficiently.

The first computer algorithm to utilize Domino Reduction was Thistlethwaite's algorithm in 1981. Due to hardware limitations back then, Domino Reduction is performed in two steps. The algorithm firstly orients the edges and then proceeds to orient the corners and separate the E-layer edges in one step. Using this approach, Domino Reduction can be reached in a maximum of 20 moves. Using two more steps after Domino Reduction, this algorithm was able to solve a cube in a maximum of 52 moves HTM.

11 years later, in 1992, Herbert Kociemba invented Kociemba's Algorithm. It's main difference from Thistlethwaite's algorithm is that the first two steps and the last two steps are combined into one step each, solving the cube in two "phases". Because of this, it is also called the Two-Phase-Algorithm. It was possible to store all positions using the more advanced technology and various optimizations like symmetry reduction described on Kociemba's website. This algorithm was able to solve Domino Reduction optimally in at most 12 moves and the whole cube in 29 moves.

Speedsolving

Although Domino Reduction is very rarely used in speedsolving, various methods have been invented to allow human solvers to reduce to a domino state quickly.

The first one was Human Thistlethwaite, an adapted version of Thistlethwaite's algorithm for humans, proposed by Ryan Heise in 2002. Most of the reduction steps are either done intuitively or using a small set of pre-made algorithms. Because of the amount of thinking required and the relatively bad ergonomics of the method, virtually no one uses Human Thistlethwaite as their main speedsolving method.

An unrelated method, Shadowslice Snow Columns, was invented in 2015 by Joseph Briggs. It starts with EOEdge, where edges are oriented and two E-slice edges are solved. The solver then proceeds by building a pseudo-pair and a pseudo-triplet and performing one of 23 algorithms. This solves the last two E-slice edges and orients the corners, effectively reducing the cube to a domino state with all E-slice edges solved. After this step, there are multiple ways to finish. The finish usually has pretty good ergonomics (R2, U, D and M moves) and makes the solve 40 to 50 moves STM long. SSC is a much more viable method for speedsolving than Human Thistlethwaite, although it's still rarely used because it drastically differs from mainstream speedsolving methods and since a good way to finish the cube after DR still needs to be found.

Although Domino Reduction might be viable for speedsolving, it is still not developed enough and too different from other methods to be adapted by more people in the near future.

Fewest moves

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See also

External links