Strucutre and Complexitiy in Planning with Unary Operators

In this paper we study the complexity of STRIPS planning when operators have a single effect. In particular, we show how the structure of the domain’s causal graph influences the complexity of planning. Causal graphs relate between preconditions and effects of domain operators. They were introduced by Williams and Nayak, who studied unary operator domains because of their direct applicability to the control of NASA’s Deep-Space One spacecraft. Williams and Nayak’s reactive planner can be trivially extended into a polynomial time plan generator in the context of tree-structured causal graphs. In this paper, we treat more complex causal graph structures, such as undirected polytrees, singly-connected networks, and general DAGs. We show that a polynomial time plan generation algorithm exists for graphs that induce an undirected polytree. More generally, we show that a certain relation exists between the number of paths in the causal graph and the complexity of planning in the associated domain.