A few months ago, I mentioned in a post called Rubik's Cube: Busted Again how Northeastern University Computer Science professor Gene Cooperman and graduate student Dan Kunkle used the Teragrid to solve Rubik's cube in 26 moves, beating the old world's record of 27 moves.

Now the Teragrid has been outdone -- by a Dr. Dobb's author, no less. Tomas Rokicki, who wrote the article An Algorithm for Compressing Space and Time, has solved the puzzle in 25 moves.

In his paper Twenty-Five Moves Suffice for Rubik's Cube, Tomas proves "this new result by separating the cube space into two billion sets, each with 20 billion elements. We then divide our attention between finding an upper bound on the distance of positions in specific sets, and combining those results to calculate an upper bound on the full cube space." Solving the problem took about 1500 hours on a Q6600 CPU running at 1.6ghz with 8GB of RAM.

The approach Tomas took is based on Kociemba's algorithm, which he then extended.  Tomas also converted Kociemba's solving algorithm into a set solver that solves billions of positions at a time. And he used simple greedy algorithms to pick sets to solve. But all of this is described in his paper.

Congratulations Tomas. Now on to 24 moves.