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

  • Authors:

  • Omer Giménez;Anders Jonsson

  • Affiliations:

  • Dept. de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Barcelona, Spain;Dept. of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain

  • Venue:
  • Journal of Artificial Intelligence Research
  • Year:
  • 2009

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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 Ckn 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 Ckn to cases k = 3 and k = 4 only, since C2n is known to be tractable.