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Reports Year : 2000

On Reconfiguring Tree Linkages: Trees can lock


It has recently been shown that any simple (i.e. nonintersecting) polygonal chain in the plane can be reconfigured to lie on a straight line, and any simple polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two simple configurations that are not connected by a motion that preserves simplicity throughout the motion. Indeed, we prove that an $N$-link tree can have $2^{\Omega(N)}$ equivalence classes of configurations.


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Dates and versions

inria-00099329 , version 1 (26-09-2006)


  • HAL Id : inria-00099329 , version 1


Thérèse Biedl, Erik Demaine, Martin Demaine, Sylvain Lazard, Anna Lubiw, et al.. On Reconfiguring Tree Linkages: Trees can lock. [Intern report] A00-R-388 || biedl00a, 2000, 16 p. ⟨inria-00099329⟩
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