eng
Schloss Dagstuhl β Leibniz-Zentrum fΓΌr Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-03-03
44:1
44:14
10.4230/LIPIcs.STACS.2023.44
article
An πͺ(3.82^k) Time FPT Algorithm for Convex Flip Distance
Li, Haohong
1
Xia, Ge
1
Department of Computer Science, Lafayette College, Easton, PA, USA
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 πͺ(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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol254-stacs2023/LIPIcs.STACS.2023.44/LIPIcs.STACS.2023.44.pdf
Flip distance
Rotation distance
Triangulations
Exact algorithms
Parameterized complexity