Motion planning with pulley, rope, and baskets

Authors Christian E.J. Eggermont, Gerhard J. Woeginger

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Christian E.J. Eggermont
Gerhard J. Woeginger

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Christian E.J. Eggermont and Gerhard J. Woeginger. Motion planning with pulley, rope, and baskets. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 374-383, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


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.
  • planning and scheduling; computational complexity


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