# 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}
}
• Published in ESA 2 September 2013
• Mathematics
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…
10 Citations
Flip Distance Between Triangulations of a Simple Polygon is NP-Complete
• Mathematics, Computer Science
Discret. Comput. Geom.
• 2015
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
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
• Computer Science
MFCS
• 2017
The backtracking strategy and the underlying property of the flip sequence are applied and it is proved that the length of the action sequence for the algorithm is bounded by $2|G|$.
Constant-Work-Space Algorithms for Shortest Paths in Trees and Simple Polygons
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J. Graph Algorithms Appl.
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Eccentricities in the flip-graphs of polygons
Consider a convex polygon $\pi$ with $n$ vertices. The flip-graph of $\pi$ is the graph whose vertices are the triangulations of $\pi$ and whose edges correspond to flips between them. The
Shortest Reconfiguration of Perfect Matchings via Alternating Cycles
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ESA
• 2019
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.
The Perfect Matching Reconfiguration Problem
• Mathematics
MFCS
• 2019
It is proved that the perfect matching reconfiguration problem is PSPACE-complete even for split graphs and for bipartite graphs of bounded bandwidth with maximum degree five, and that the problem is solvable in polynomial time.
Differential Privacy via Weighted Sampling Set Cover
• Computer Science, Mathematics
• 2016
A special sampling via set cover model is proposed in this article, which builds a multidimensional composite marginal tables set as a new middleware in differential privacy model, and the accuracy of data query is improved.
Reconfiguration and combinatorial games
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
• Computer Science
ArXiv
• 2013
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.

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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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