The complexity of (un)folding

Authors:
Helmut Alt;Christian Knauer;Günter Rote;Sue Whitesides
Affiliations:
Freie Universitat Berlin, Takustraaye 9, D--14195 Berlin, Germany;Freie Universitat Berlin, Takustraaye 9, D--14195 Berlin, Germany;Freie Universitat Berlin, Takustraaye 9, D--14195 Berlin, Germany;McGill University, Montreal, Canada
Venue:
Proceedings of the nineteenth annual symposium on Computational geometry
Year:
2003

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Abstract

We consider the problem of reconfiguring a linkage of rigid straight segments from a given start to a given target position with a continuous nonintersecting motion. The problem is nontrivial even for trees in two dimensions since it is known that not all configurations can be reconfigured to a straight position. We show that deciding reconfigurability for trees in two dimensions and for chains in three dimensions is PSPACE-complete.