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

TL;DR

This paper presents the 2026 CG:SHOP Challenge focused on identifying a central triangulation that minimizes total flip distances to given triangulations, advancing understanding of flip operations in computational geometry.

Contribution

It introduces a new challenge problem in computational geometry, defining the task of finding a central triangulation under parallel flip operations and providing a benchmark for future research.

Findings

Defined the problem of central triangulation under parallel flips

Established a benchmark for computational geometry algorithms

Provided initial results and insights from the challenge

Abstract

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