Flip distance between triangulations of a planar point set is APX-hard

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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