Solving Atomix with Pattern Databases

In this paper we study the application of pattern databases (PDBs) to optimally solving Atomix. Atomix is a puzzle, where one has to assemble a molecule from atoms by sliding moves. It is particularly challenging, because the slides makes it hard to create admissible heuristics, and state-of-the-art heuristics are rather uninformed. A pattern database (PDB) stores solutions to an abstract version of a state space problem. An admissible lower bound for a given state is obtained by decomposing it into abstract states and combining their pre-computed solutions. Different from other puzzles a pattern in Atomix cannot be simply obtained by omitting pieces from the puzzle. We also study the search algorithm Partial Expansion A*'s application to Atomix, as a reduced-memory alternative to A*. Experiments show our method solves more instances and significantly improves current lower bounds, running times and node expansions compared to the best solution in the literature.