Motion planning with pulley, rope, and baskets

Christian E.J. Eggermont , Gerhard J. Woeginger

We study a motion planning problem where items have to be transported from the top room of a tower to the bottom of the tower, while simultaneously other items have to be transported into the opposite direction. Item sets are moved in two baskets hanging on a rope and pulley. To guarantee stability of the system, the weight difference between the contents of the two baskets must always stay below a given threshold. We prove that it is Pi-2-p-complete to decide whether some given initial situation of the underlying discrete system can lead to a given goal situation. Furthermore we identify several polynomially solvable special cases of this reachability problem, and we also settle the computational complexity of a number of related questions.

Mots clés: planning and scheduling; computational complexity

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Christian E.J. Eggermont, Gerhard J. Woeginger. Motion planning with pulley, rope, and baskets. STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Feb 2012, Paris, France. pp.374-383. ⟨hal-00678160⟩