Paper by Martin L. Demaine

Reference:

Therese Biedl, Erik Demaine, Martin Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Steve Robbins, Ileana Streinu, Godfried Toussaint, and Sue Whitesides, “On Reconfiguring Tree Linkages: Trees can Lock”, Technical Report SOCS-00.7, School of Computer Science, McGill University, September 2000.

Abstract:

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^Ω(N) equivalence classes of configurations.

Comments:

This paper is also available as arXiv:cs.CG/9910024 of the Computing Research Repository (CoRR).

Length:

The paper is 16 pages.

Availability:

The paper is available in PostScript (412k) and gzipped PostScript (88k).

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Related papers:

LockedTreeDAM (A Note on Reconfiguring Tree Linkages: Trees can Lock)

CCCG98c (On Reconfiguring Tree Linkages: Trees can Lock)

Related webpages:

Erik Demaine's Carpenter's Rule Theorem