State-Variable Planning Under Structural Restrictions: Algorithms and Complexity

Computationally tractable planning problems reported in the literature so far have almost exclusively been de ned by syntactical restrictions. To better exploit the inherent structure in problems, it is probably necessary to study also structural restrictions on the underlying state-transition graph. The exponential size of this graph, though, makes such restrictions costly to test. Hence, we propose an intermediate approach, using a state variable model for planning and de ning restrictions on the separate state-transition graphs for each state variable. We identify such restrictions which can tractably be tested and we present a planning algorithm which is correct and runs in polynomial time under these restrictions. The algorithm has been implemented an it outperforms Graphplan on a number of test instances. In addition, we present an exhaustive map of the complexity results for planning under all combinations of four previously studied syntactical restrictions and our ve new structural restrictions. This complexity map considers both the optimal and non-optimal plan generation problem.