Flip Distance between Triangulations of a Simple Polygon is NP-Complete

@inproceedings{Aichholzer2013FlipDB,
  title={Flip Distance between Triangulations of a Simple Polygon is NP-Complete},
  author={Oswin Aichholzer and Wolfgang Mulzer and Alexander Pilz},
  booktitle={ESA},
  year={2013}
}
Let T be a triangulation of a simple polygon. A flip in T is the operation of removing one diagonal of T and adding a different one such that the resulting graph is again a triangulation. The flip distance between two triangulations is the smallest number of flips required to transform one triangulation into the other. For the special case of convex polygons, the problem of determining the shortest flip distance between two triangulations is equivalent to determining the rotation distance… 
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10 Citations

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Flip Distance Between Triangulations of a Simple Polygon is NP-Complete
TLDR
It is shown that computing the flip distance between two triangulations of a simple polygon is NP-hard, which complements a recent result that shows APX-hardness of determining the flip Distance between two Triangulation of a planar point set.
A Note on the Flip Distance Problem for Edge-Labeled Triangulations
TLDR
It is shown in this note that the flip distance problem is APX- hard for edge-labeled triangulations of point sets and NP-hard for triangulation of simple polygons.
An Improved FPT Algorithm for the Flip Distance Problem
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Eccentricities in the flip-graphs of polygons
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It is proved that the shortest reconfiguration problem of perfect matchings via alternating cycles is NP-hard even when a given graph is planar or bipartite, but it can be solved in polynomial time when the graph is outerplanar.
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Cette these explore des problematiques liees aux jeux. Les jeux qui nous interessent sont ceux pour lesquels il n'y a pas d'information cachee: tout les joueurs ont acces a toute l'information…
Practical Reduction of Edge Flip Sequences in Two-Dimensional Triangulations
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The new approach is founded on the assignment of labels to identify the edges, with a property of label transfer during a flip that gives a meaning to the tracking of an edge in a sequence of flips and offers the exploitation of very simple combinatorial properties.

References

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Flip Distance Between Triangulations of a Simple Polygon is NP-Complete
TLDR
It is shown that computing the flip distance between two triangulations of a simple polygon is NP-hard, which complements a recent result that shows APX-hardness of determining the flip Distance between two Triangulation of a planar point set.
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