Parameterized Complexity of Optimal Planning: A Detailed Map

Martin Kronegger, Andreas Pfandler, Reinhard Pichler

Abstract: The goal of this paper is a systematic parameterized complexity analysis of different variants of propositional STRIPS planning. We identify several natural problem parameters and study all possible combinations of 9 parameters in 6 different settings. These settings arise, for instance, from the distinction if negative effects of actions are allowed or not. We provide a complete picture by establishing for each case either paraNP-hardness (i.e., the parameter combination does not help) or W[t]-completeness with t ∈ {1, 2} (i.e., fixed-parameter intractability), or FPT (i.e., fixed-parameter tractability).