Stronger abstraction heuristics through perimeter search

Perimeter search is a bidirectional search algorithm consisting of two phases. In the first phase, a limited regression search computes the perimeter, a region which must necessarily be passed in every solution. In the second phase, a heuristic forward search finds an optimal plan from the initial state to the perimeter. The drawback of perimeter search is the need to compute heuristic estimates towards every state on the perimeter in the forward phase. We show that this limitation can be effectively overcome when using pattern database (PDB) heuristics in the forward phase. The combination of perimeter search and PDB heuristics has been considered previously by Felner and Ofek for solving combinatorial puzzles. They claimed that, based on theoretical considerations and experimental evidence, the use of perimeter search in this context offers "limited or no benefits". Our theoretical and experimental results show that this assessment should be revisited.