Planning over Chain Causal Graphs for Variables with Domains of Size 5 Is NP-Hard

O. Giménez and A. Jonsson

Recently, considerable focus has been given to the problem of determining the boundary between tractable and intractable planning problems. In this paper, we study the complexity of planning in the class Cn of planning problems, characterized by unary operators and directed path causal graphs. Although this is one of the simplest forms of causal graphs a planning problem can have, we show that planning is intractable for Cn (unless P = NP), even if the domains of state variables have bounded size. In particular, we show that plan existence for Cn>k is NP-hard for k >= 5 by reduction from CNFSAT. Here, k denotes the upper bound on the size of the state variable domains. Our result reduces the complexity gap for the class Cnk to cases k = 3 and k = 4 only, since Cn2 is known to be tractable.

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