# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, September 25, 2012, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Alexander Pilz (Graz University of Technology)

## Flip Distance Between Triangulations of a Simple Polygon is NP-Complete

A flip in a triangulation is the operation of removing one edge of the triangulation and adding a diffrent one such that the resulting graph is again a triangulation. The flip distance between two triangulations is the smallest number of flips that is necessary to transform one triangulation into the other. We show that computing the shortest flip distance between two triangulations of a simple polygon is NP-hard. This complements a recent result that shows NP-hardness of determining the flip distance between two triangulations of a planar point set. For the special case of convex polygons, the problem is equivalent to the rotation distance of binary trees, a central problem which is still open after over 25 years of intensive study. (Joint work with Oswin Aichholzer and Wolfgang Mulzer.)

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