1.6-Bit Pattern Databases

We present a new technique to compress consistent pattern databases without loss of information by storing the heuristic estimate modulo three, requiring only two bits per entry, or in a more compact representation only 1.6 bits. This enables us to store a pattern database with four or five times as many entries in the same amount of memory as an uncompressed pattern database. We compare both methods to the best existing compression methods for the Top-Spin puzzle, Rubik’s cube, the 4peg Towers of Hanoi Problem, and the 24-puzzle. For the Top-Spin puzzle and Rubik’s cube we also compare our best implementation to the respective state of the art solvers. This compression technique is most useful where methods for lossy compression fail, for example where patterns mapping to adjacent entries in the pattern database are not reachable from each other by one move, such as in the Top-Spin puzzle and Rubik’s cube.