The Computational Complexity of Motion Planning
Jeff Hartline, Ran Libeskind-Hadas · SIAM Review · 2003
In this paper we show that a generalization of a popular motion planning puzzle called Lunar Lockout is computationally intractable. In particular, we show that the problem is PSPACE-complete. We begin with a review of NP-completeness and polynomial-time reductions, introduce the class PSPACE, and motivate the significance of PSPACE-complete problems. Afterwards, we prove that determining whether a given instance of a generalized Lunar Lockout puzzle is solvable is PSPACE-complete.