Polygonal chains cannot lock in 4D (1999) [24 citations — 0 self]
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by Roxana Cocan
In Proc. 11th Canad. Conf. Comput. Geom
ftp://cs.smith.edu/pub/orourke.papers/chains4d.ps.gz
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@INPROCEEDINGS{Cocan99polygonalchains,author = {Roxana Cocan},
title = {Polygonal chains cannot lock in 4D},
booktitle = {In Proc. 11th Canad. Conf. Comput. Geom},
year = {1999},
pages = {5--8}
}
Years of Citing Articles
Abstract:
We prove that, in all dimensions d 4, every simple open polygonal chain and every tree may be straightened, and every simple closed polygonal chain may be convexified. These reconfigurations can be achieved by algorithms that use polynomial time in the number of vertices, and result in a polynomial number of "moves. " These results contrast to those known for d = 2, where trees can "lock, " and for d = 3, where open and closed chains can lock.
Citations
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| 38 | Algorithmic motion planning – Sharir - 2004 |
| 36 | Locked and unlocked polygonal chains in 3D – Biedl, Demaine, et al. - 1999 |
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| 29 | Reconfiguring closed polygonal chains in Euclidean d-space. Discrete – Lenhart, Whitesides - 1995 |
| 20 | Introduction to Knot Theory – Crowell, Fox - 1963 |
| 15 | Computational Real Algebraic Geometry – Mishra - 1997 |
| 10 | Stretching chords of space curves – Sallee - 1973 |
| 4 | Projective Geometry – Samuel - 1988 |
| 1 | BDD + 98 – McGraw-Hill, London - 1979 |
| 1 | Polygonal chains cannot lock in 4D. Undergraduate thesis, Smith College – Cocan - 1999 |
| 1 | A new class of stuck unknots – Toussaint - 1999 |
