Completeness and Optimality Preserving Reduction for Planning

Traditional AI search methods search in a state space typically modelled as a directed graph. Prohibitively large sizes of state space graphs make complete or optimal search expensive. A key observation, as exemplified by the SAS+ formalism for planning, is that most commonly a state-space graph can be decomposed into subgraphs, linked by constraints. We propose a novel space reduction algorithm that exploits such structure. The result reveals that standard search algorithms may explore many redundant paths. Our method provides an automatic way to remove such redundancy. At each state, we expand only the subgraphs within a dependency closure satisfying certain sufficient conditions instead of all the subgraphs. Theoretically we prove that the proposed algorithm is completeness-preserving as well as optimality-preserving. We show that our reduction method can significantly reduce the search cost on a collection of planning domains.