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Motion Planning with Pulley, Rope, and Baskets

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Abstract

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 in 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 \(\varPi_{2}^{p}\)-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.

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Acknowledgements

This research has been supported by the Netherlands Organisation for Scientific Research (NWO), grant 639.033.403, and by DIAMANT (an NWO mathematics cluster). Gerhard Woeginger acknowledges support by the Alexander von Humboldt Foundation, Bonn, Germany.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, Netherlands

    Christian E. J. Eggermont & Gerhard J. Woeginger

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  1. Christian E. J. Eggermont
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  2. Gerhard J. Woeginger
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Correspondence to Gerhard J. Woeginger.

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Eggermont, C.E.J., Woeginger, G.J. Motion Planning with Pulley, Rope, and Baskets. Theory Comput Syst 53, 569–582 (2013). https://doi.org/10.1007/s00224-013-9445-4

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