Central Triangulation under Parallel Flip Operations: The CG:SHOP Challenge 2026
This addresses a computational geometry challenge for researchers and practitioners, but appears incremental as it focuses on a specific optimization problem within triangulations.
The paper tackled the problem of finding a central triangulation that minimizes the sum of parallel flip distances to a set of given triangulations, as part of the CG:SHOP Challenge 2026, but did not report specific results or numbers.
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