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

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

Figures (6)

• Figure 1: Illustrative examples of (a) sequential and (b) parallel flip operations.
• Figure 2: Three triangulations $T_1,T_2,T_3$ and a central triangulation $C$ with objective value $7$.
• Figure 3: An example random instance with 15.0 points and 4.0 triangulations for which a center is to be found.
• Figure 4: An example woc instance with 45.0 points and 4.0 triangulations for which a center is to be found.
• Figure 5: Mean ratio to the best solution for the top 5 teams, by instance class. A value of 1.0 means the team matched the best known solution on every instance in that class.