Abstract

We present solutions of benchmark instances to the solitaire computer game Atomix found with different heuristic search methods. The problem is PSPACE-complete. An implementation of the heuristic algorithm A * is presented that needs no priority queue, thereby having very low memory overhead. The limited memory algorithm IDA * is handicapped by the fact that, due to move transpositions, duplicates appear very frequently in the problem space; several schemes of using memory to mitigate this weakness are explored, among those, “partial” schemes which trade memory savings for a small probability of not finding an optimal solution. Even though the underlying search graph is directed, backward search is shown to be viable, since the branching factor can be proven to be the same as for forward search.

Citations