Central Triangulation under Parallel Flip Operations: The CG:SHOP Challenge 2026

Authors: Oswin Aichholzer, Joseph Dorfer, Sándor P. Fekete, Phillip Keldenich, Peter Kramer, Stefan Schirra

We give an overview of the 2026 Computational Geometry Challenge targeting the problem of finding a Central Triangulation under Parallel Flip Operations in triangulations of point sets. A flip is the parallel exchange of a set of edges in a triangulation with opposing diagonals of the convex quadrilaterals containing them. The challenge objective was, given a set of triangulations of a fixed point set, to determine a central triangulation with respect to parallel flip distances. More precisely, this asks for a triangulation that minimizes the sum of flip distances to all elements of the input