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Mover Problems

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Thirty Essays on Geometric Graph Theory

Abstract

Leo Moser asked what is the region of largest area that can be moved around a right-angled corner in a corridor of unit width? Similarly, what is the region of largest area that can be reversed in a T junction made up of roads of unit width? Can a specific 3-dimensional object pass through a given door? Our survey aims at showing that mover problems are no less challenging even if there are no obstacles other than the objects themselves, but there are many objects to move. We survey some recent results on motion planning and reconfiguration for systems of multiple objects and for modular systems with applications in robotics, and collect some open problems coming out of this line of research.

Supported in part by NSF CAREER grant CCF-0444188 and NSF grant DMS-1001667.

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Acknowledgements

The author is grateful to his collaborators, S. Bereg, G. Călinescu, M. Jiang, J. Pach, I. Suzuki, and M. Yamashita, for allowing him to borrow some material from their respective joint works.

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  1. Department of Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI, USA

    Adrian Dumitrescu

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  1. Adrian Dumitrescu
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Correspondence to Adrian Dumitrescu .

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  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    János Pach (Chair of Combinatorial Geometry) (Chair of Combinatorial Geometry)

  2. École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    János Pach (Chair of Combinatorial Geometry) (Chair of Combinatorial Geometry)

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Dumitrescu, A. (2013). Mover Problems. In: Pach, J. (eds) Thirty Essays on Geometric Graph Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0110-0_11

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