Flip distance between two triangulations of a point set is NP-complete

Anna Lubiw, Vinayak Pathak
2015 Computational geometry  
Given two triangulations of a convex polygon, computing the minimum number of flips required to transform one to the other is a long-standing open problem. It is not known whether the problem is in P or NP-complete. We prove that two natural generalizations of the problem are NP-complete, namely computing the minimum number of flips between two triangulations of (1) a polygon with holes; (2) a set of points in the plane.
doi:10.1016/j.comgeo.2014.11.001 fatcat:ebnw4dsrhfehvluhxqdzxqsnne