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

2026-03-19

AI Summary

This work formalizes and investigates the centrality problem in triangulations: given a set of input triangulations, it seeks a central triangulation that minimizes the sum of parallel flip distances to all inputs. As an NP-hard problem and the core challenge of the CG:SHOP 2026 algorithm competition, it is addressed through an integrated approach combining computational geometry, graph-theoretic modeling, and combinatorial optimization. Leveraging structural properties of parallel flips, the study designs efficient search and approximation algorithms. This paper presents the first systematic formulation of the problem, fostering interdisciplinary connections between discrete geometry and combinatorial optimization. By catalyzing diverse solution strategies through the competition, it establishes a practical benchmark for algorithmic performance in this emerging domain.

Technology Category

Search and Optimization: Combinatorial OptimizationConstraint Satisfaction and Optimization: Distributed CSP/OptimizationKnowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsWeb Mining and Content Analysis: Models for Web evolution

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

Problem

• Central Triangulation
• Parallel Flip Operations
• Triangulations
• Flip Distance
• Point Sets

Innovation

• parallel flip
• central triangulation
• triangulation distance
• computational geometry
• CG:SHOP challenge