Difference between revisions of "Domino Reduction"

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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.
 
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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== Fewest move solving ==
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Domino Reduction in an [[FMC]] context has been mentioned as early as 2007[https://www.speedsolving.com/threads/fewest-moves-tips-and-techniques.1566/#post-15795]. However, it only started to be widely used in 2019. In that year, Domino Reduction became so popular that it was adopted by virtually all top solvers as their main way to do FMC because it usually yields better results than standard blockbuilding, allowing for consistent sub-30 solves in the hands of an expert. The technique also lead to multiple records in that year, such as [[Harry Savage]]'s [https://www.speedsolving.com/threads/harry-savage-17-fmc-single-sebastiano-tronto-24-00-mean.72299/ 17 move WR single] [[Sebastiano Tronto]]'s [https://www.speedsolving.com/threads/wrs-sebastiano-tronto-22-mean-and-16-single-at-fmc-2019.74270/ 16 move WR single]. Inspired by the records and frustrated by the lack of documentation, [[Alexandros Fokianos]] and [[Tommaso Raposio]] documented Domino Reduction for FMC in [https://www.speedsolving.com/threads/a-domino-reduction-guide-for-fmc.74828/ "A Domino Reduction Guide"] on August 7, 2019. Because the guide explains Domino Reduction in great detail, only an overview is given here.
  
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=== Performing Domino Reduction ===
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=== Finishing after Domino Reduction ===
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=== Partial Domino Reduction ===
 
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== External links ==
 
== External links ==
* [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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* [https://www.speedsolving.com/threads/a-domino-reduction-guide-for-fmc.74828/ A Domino Reduction Guide for FMC by Alexandros Fokianos and Tommaso Raposio]
 
* [http://kociemba.org/cube.htm Kociemba's website, including his Two-Phase-Algorithm]
 
* [http://kociemba.org/cube.htm Kociemba's website, including his Two-Phase-Algorithm]
 
* [http://kociemba.org/math/distribution.htm Kociemba's distribution of moves required for DR]
 
* [http://kociemba.org/math/distribution.htm Kociemba's distribution of moves required for DR]

Revision as of 15:56, 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 move solving

Domino Reduction in an FMC context has been mentioned as early as 2007[1]. However, it only started to be widely used in 2019. In that year, Domino Reduction became so popular that it was adopted by virtually all top solvers as their main way to do FMC because it usually yields better results than standard blockbuilding, allowing for consistent sub-30 solves in the hands of an expert. The technique also lead to multiple records in that year, such as Harry Savage's 17 move WR single Sebastiano Tronto's 16 move WR single. Inspired by the records and frustrated by the lack of documentation, Alexandros Fokianos and Tommaso Raposio documented Domino Reduction for FMC in "A Domino Reduction Guide" on August 7, 2019. Because the guide explains Domino Reduction in great detail, only an overview is given here.

Performing Domino Reduction

Scramble 01.jpg This page is under construction!
One or more of our members are currently working on this page.
Come back in a few days and it will hopefully be completed by then.

Finishing after Domino Reduction

Scramble 01.jpg This page is under construction!
One or more of our members are currently working on this page.
Come back in a few days and it will hopefully be completed by then.

Partial Domino Reduction

Scramble 01.jpg This page is under construction!
One or more of our members are currently working on this page.
Come back in a few days and it will hopefully be completed by then.

See also

External links