Moving coins

Authors:
Manuel Abellanas;Sergey Bereg;Ferran Hurtado;Alfredo García Olaverri;David Rappaport;Javier Tejel
Affiliations:
Universidad Politécnica de Madrid, Spain;University of Texas at Dallas;Universitat Politècnica de Catalunya, Spain;Universidad de Zaragoza, Spain;Queen's University, Canada;Universidad de Zaragoza, Spain
Venue:
Computational Geometry: Theory and Applications - Special issue on the Japan conference on discrete and computational geometry 2004
Year:
2006

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Abstract

We consider combinatorial and computational issues that are related to the problem of moving coins from one configuration to another. Coins are defined as non-overlapping discs, and moves are defined as collision free translations, all in the Euclidean plane. We obtain combinatorial bounds on the number of moves that are necessary and/or sufficient to move coins from one configuration to another. We also consider several decision problems related to coin moving, and obtain some results regarding their computational complexity.