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# An πͺ(3.82^k) Time FPT Algorithm for Convex Flip Distance

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LIPIcs.STACS.2023.44.pdf
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## Cite As

Haohong Li and Ge Xia. An πͺ(3.82^k) Time FPT Algorithm for Convex Flip Distance. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 44:1-44:14, Schloss Dagstuhl β Leibniz-Zentrum fΓΌr Informatik (2023)
https://doi.org/10.4230/LIPIcs.STACS.2023.44

## Abstract

Let P be a convex polygon in the plane, and let T be a triangulation of P. An edge e in T is called a diagonal if it is shared by two triangles in T. A flip of a diagonal e is the operation of removing e and adding the opposite diagonal of the resulting quadrilateral to obtain a new triangulation of P from T. The flip distance between two triangulations of P is the minimum number of flips needed to transform one triangulation into the other. The Convex Flip Distance problem asks if the flip distance between two given triangulations of P is at most k, for some given parameter k β β. We present an FPT algorithm for the Convex Flip Distance problem that runs in time πͺ(3.82^k) and uses polynomial space, where k is the number of flips. This algorithm significantly improves the previous best FPT algorithms for the problem.

## Subject Classification

##### ACM Subject Classification
• Theory of computation β Computational geometry
• Theory of computation β Parameterized complexity and exact algorithms
##### Keywords
• Flip distance
• Rotation distance
• Triangulations
• Exact algorithms
• Parameterized complexity

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## References

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