Planning over chain causal graphs for variables with domains of size 5 is NP-hard

Abstract

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 ℂnk is NP-hard for k ≥ 5 by reduction from CNF-SAT. 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. © 2009 AI Access Foundation. All rights reserved.