Flip Distance Between Two Triangulations of a Point-Set is NP-complete

2012/05/11 by Anna Lubiw, Vinayak Pathak, Lubiw, Anna +1 · 2 citations
Computer Science · #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Computer and information sciences #Optimization and Search Problems

paper · pdf · doi:10.48550/arxiv.1205.2425

openalex publication_date 2012/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Monotonically Decreasing the Number of Directed 3-Cycles via Edge-Flips?
• Constrained Flips in Plane Spanning Trees

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