Reduction, also known as Redux, is the current dominant group of methods for big cubes speedsolving, and the dominant method for 5x5x5+ that solves centers and matches edges to "reduce" the puzzle to a 3x3x3.
Almost every speedcuber uses the reduction method for 5x5 and bigger cubes. Reduction was formerly the dominantly used method for 4x4 as well, however the Yau method has recently taken over. It can also be used as a beginner's method.
The Freeslice method is a variant of reduction, the most common variant of Reduction used in speedsolving and also the most common big cubes method. The only difference between the Reduction and the Freeslice method is the edge pairing stage because this is done via Freeslice edge pairing in the Freeslice method. Although not really a method in its own right, calling Reduction with Freeslice edge pairing the "Freeslice method" is common to prevent mistaking it for the Reduction method used by beginners (where dedges are formed in pairs of two or sometimes even only one).
Comparison with other methods
Others methods such as Cage have been used to attain fast times on very large cube cube simulators (on very big cubes there are almost only centers to solve and most time is spent looking for them so the method used does not matter that much).
Reduction in other puzzles
The idea of reduction is applicable to other puzzles, where it may be easier to manipulate a puzzle so it functions as a simpler sub-puzzle. In most cases, reduction is used to simplify the puzzle by grouping pieces first, instead of directly solving pieces into their correct positions.
The idea of reduction can sometimes be formalized as effectively as placing a puzzle into a smaller subgroup. Thistlethwaite's algorithm was based on several iterative reductions, and most fast computer solvers essentially use those approaches.
Although most solving methods involve steps that reduce the left-over puzzle portion, simply solving the puzzle into "less of a mess" (such as "reducing" a cube to the LL with Petrus) is not commonly considered reduction. The term is more applied to solving a puzzle into a differently interpretable puzzle, which is normally solved without resort to treating it like the original puzzle (with notable exceptions, such as Parity).
- bigcubes.com Tutorial
- Meep's website
- Bob Burton's 4x4 algs
- 4x4 Begginers tutorial
- SirWaffle's 5x5 Last two centers tutorial
- SirWaffle's 5x5 Last two edges tutorial
- Cyoubx's 5x5 tips
- Kevin Hays's 5x5 tips and tricks
- Feliks's 5x5 walktrough solves
- Kevin Hays's 6x6 walktrough solves
- JRcuber's 5x5 walktrough solves
- JRcuber's 7x7 walktrough solves