ESA 2013: Algorithms – ESA 2013 pp 13-24

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

• Oswin Aichholzer
• Wolfgang Mulzer
• Alexander Pilz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)

## Abstract

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 between two binary trees, a central problem which is still open after over 25 years of intensive study.

We show that computing the flip distance between two triangulations of a simple polygon is NP-complete. This complements a recent result that shows APX-hardness of determining the flip distance between two triangulations of a planar point set.

## Keywords

Binary Tree Convex Polygon Full Version Simple Polygon Outerplanar Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Oswin Aichholzer
• 1
• Wolfgang Mulzer
• 2
• Alexander Pilz
• 1
1. 1.Institute for Software TechnologyGraz University of TechnologyAustria
2. 2.Institute of Computer ScienceFreie Universität BerlinGermany