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arXiv · 1206.3179

Flip Distance Between Triangulations of a Planar Point Set is APX-Hard

Alexander Pilz
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Abstract

In this work we consider triangulations of point sets in the Euclidean plane, i.e., maximal straight-line crossing-free graphs on a finite set of points. Given a triangulation of a point set, an edge flip is the operation of removing one edge and adding another one, such that the resulting graph is again a triangulation. Flips are a major way of locally transforming triangular meshes. We show that, given a point set $S$ in the Euclidean plane and two triangulations $T_1$ and $T_2$ of $S$, it is an APX-hard problem to minimize the number of edge flips to transform $T_1$ to $T_2$.

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Alexander Pilz. 2015-05-12. Flip Distance Between Triangulations of a Planar Point Set is APX-Hard. https://doi.org/10.1016/j.comgeo.2014.01.001

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