GPU-acceleration of optimal permutation-puzzle solving

Abstract

We first investigate parallelization of Rubik's cube optimal solver, especially for acceleration by GPU. To examine its efficacy, we implement a simple solver based on Korf's algorithm, with which CPU and GPU collaborate in IDA* algorithm and a large number of GPU cores are utilized for speedup instead of a huge distance table used for pruning. Empirical studies succeeded to attain sufficient speedup by GPU-acceleration. There are many other similar puzzles of so-called permutation puzzles. The puzzle solving, i.e., restoring the original ordered state from a scrambled one is equivalent to the path-finding in the Cayley graph of the permutation group. We generalize the method used for Rubik's cube to much smaller problems, and examine its efficacy. The focus of our research interest is how efficient the parallel path-finding can be and whether the use of a large number of cores substitutes for a large distance table used for pruning, in general.