Paper by Erik D. Demaine

Reference:

Sergio Cabello, Erik D. Demaine, and Günter Rote, “Planar Embeddings of Graphs with Specified Edge Lengths”, in Proceedings of the 11th Symposium on Graph Drawing (GD 2003), Lecture Notes in Computer Science, volume 2912, Perugia, Italy, September 21–24, 2003, pages 283–294.

BibTeX

@InProceedings{PlanarEmbedding_GD2003,
  AUTHOR        = {Sergio Cabello and Erik D. Demaine and G\"unter Rote},
  TITLE         = {Planar Embeddings of Graphs with Specified Edge Lengths},
  BOOKTITLE     = {Proceedings of the 11th Symposium on Graph Drawing
                   (GD 2003)},
  bookurl       = {http://www.gd2003.org/},
  VOLUME        = 2912,
  SERIES        = {Lecture Notes in Computer Science},
  SERIESURL     = {http://www.springer.de/comp/lncs/},
  ADDRESS       = {Perugia, Italy},
  MONTH         = {September 21--24},
  YEAR          = 2003,
  PAGES         = {283--294},

  copyright     = {The paper is \copyright Springer-Verlag.},
  length        = {12 pages},
  papers        = {PlanarEmbedding_JGAA},
  doi           = {https://dx.doi.org/10.1007/978-3-540-24595-7_26},
  dblp          = {https://dblp.org/rec/conf/gd/CabelloDR03},
  comments      = {This paper is also available from <A HREF="https://doi.org/10.1007/978-3-540-24595-7_26">SpringerLink</A>.},
}

Abstract:

We consider the problem of finding a planar embedding of a (planar) graph with a prescribed Euclidean length on every edge. There has been substantial previous work on the problem without the planarity restrictions, which has close connections to rigidity theory, and where it is easy to see that the problem is NP-hard. In contrast, we show that the problem is tractable—indeed, solvable in linear time on a real RAM—for planar embeddings of planar 3-connected triangulations, even if the outer face is not a triangle. This result is essentially tight: the problem becomes NP-hard if we consider instead planar embeddings of planar 3-connected infinitesimally rigid graphs, a natural relaxation of triangulations in this context.

Comments:

This paper is also available from SpringerLink.

Copyright:

The paper is \copyright Springer-Verlag.

Length:

The paper is 12 pages.

Availability:

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PlanarEmbedding_JGAA (Planar Embeddings of Graphs with Specified Edge Lengths)