Paper by Erik D. Demaine

Reference:

Erik D. Demaine and Sarah Eisenstat, “Expansive Motions for d-Dimensional Open Chains”, in Proceedings of the 23rd Canadian Conference on Computational Geometry (CCCG 2011), Toronto, Ontario, Canada, August 10–12, 2011, to appear.

BibTeX

@InProceedings{Expansive_CCCG2011,
  AUTHOR        = {Erik D. Demaine and Sarah Eisenstat},
  TITLE         = {Expansive Motions for $d$-Dimensional Open Chains},
  BOOKTITLE     = {Proceedings of the 23rd Canadian Conference on
                   Computational Geometry (CCCG 2011)},
  bookurl       = {http://2011.cccg.ca/},
  ADDRESS       = {Toronto, Ontario, Canada},
  MONTH         = {August 10--12},
  YEAR          = 2011,
  PAGES         = {to appear},

  length        = {6 pages},
  withstudent   = 1,
  unrefereed    = 1,
  dblp          = {https://dblp.org/rec/conf/cccg/EisenstatD11},
  ee            = {http://www.cccg.ca/proceedings/2011/papers/paper96.pdf},
}

Abstract:

We consider the problem of straightening chains in d ≥ 3 dimensions, possibly embedded into higher dimensions, using expansive motions. For any d ≥ 3, we show that there is an open chain in d dimensions that is not straight and not self-touching yet has no expansive motion. Furthermore, for any Δ > 0 and d ≥ 3, we show that there is an open chain in d dimensions that cannot be straightened using expansive motions when embedded into ℝ^d × [−Δ, Δ] (a bounded extra dimension). On the positive side, we prove that any open chain in d ≥ 2 dimensions can be straightened using an expansive motion when embedded into ℝ^d + 1 (a full extra dimension).

Length:

The paper is 6 pages.

Availability:

The paper is available in PDF (308k).

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