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.
We present an FPT algorithm for the Convex Flip Distance problem that runs in
time O(3.82k) and uses polynomial space, where k is the number of flips.
This algorithm significantly improves the previous best FPT algorithms for the
problem