Complete Search of Sliding Tile Puzzles on a Personal Computer [Extended Abstract]

Abstract

The 4x4 and 8x2 Sliding Tile Puzzles have more than ten trillion solvable states, making complete brute force search very challenging: best existing solutions take weeks to run or require expensive hardware. We propose and implement a set of optimizations of the frontier search algorithm, that are efficient on a modern personal computer. We run a number of complete searches, each taking about 3 days on our hardware, for both puzzles in single-tile and multi-tile metrics, verifying previously known results about the radiuses of the puzzles. We also discover that the diameter of the 4x4 Puzzle is 80 single-tile moves, and the radius of the 8x2 Puzzle is 57 multi-tile moves.