Half Turn Reduction
Half Turn Reduction or HTR is a technique invented by Morwen Thistlethwaite. It is employed by computer algorithms, speedsolvers and fewest move solvers to bring the 3x3x3 cube into the Square group so only half turns are required to solve the cube. This is accomplished by separating the pieces so that each side contains at most two colors which must be opposite to each other. The most practical way to do this is to perform Domino Reduction on two axes while also avoiding diagonal corner permutation. After the reduction, the cube is always at most 15 moves away from solved.
Half Turn Reduction was initially invented to allow computer algorithms to solve the cube efficiently.
It was first used in 1981 in Thistlethwaite's algorithm, where HTR was the third step. The algorithm was able to perform HTR in 35 moves HTM, resulting in a guaranteed maximum of 52 moves for solving any given legal state.
Although attempts like Human Thistlethwaite have been made to use HTR in speedsolving, no one who mains a method based around HTR for speedsolving is known. This is mainly due to the bad ergonomics in the finish (half turns usually take longer to perform than their quarter equivalents and regrips tend to be common) and the reduction being too complicated because diagonal CP needs to be prevented and since the cube has to be reduced to a Domino state before HTR.
Fewest move solving
Half Turn Reduction is sometimes employed in FMC to finish the solve after Domino Reduction. It was used to set Harry Savage's 17 move WR single and is also described in Alexandros Fokianos' and Tommaso Raposio's "A Domino Reduction Guide". The following should only serve as an overview while the linked guide should be consulted for more in-depth information.
Performing Half Turn Reduction
After Domino Reduction, FMC solvers usually tend to perform Half Turn Reduction when the corners are "good", i.e. easy to solve. This is due to the fact that in such situations, diagonal CP after HTR tends to be very rare.
Finishing after Half Turn Reduction