ETH Flippers Approach to Parallel Reconfiguration of Triangulations: SAT formulation and Heuristics

TL;DR

This paper presents the ETH Flippers team's algorithms for the CG:SHOP 2026 Challenge, combining SAT-based exact solutions and heuristics to efficiently reconfigure triangulations with proven optimality in many cases.

Contribution

It introduces a hybrid approach using SAT formulation and heuristics for parallel triangulation reconfiguration, achieving high-quality solutions and ranking second overall.

Findings

Ranked second overall in the challenge

Proved optimal solutions for 186 out of 250 instances

Combined SAT encoding with heuristics for large instances

Abstract

We describe the algorithms used by the ETH Flippers team in the CG:SHOP 2026 Challenge. Each instance consists of a set of triangulations on a common point set, and the objective is to find a central triangulation that minimizes the total parallel flip distance to the input set. Our strategy combines an exact solver for small and medium-sized instances with a suite of heuristics for larger instances. For the exact approach, we formulate the problem as a SAT instance with XOR clauses to model edge transitions across multiple rounds, further optimized by lower bounds derived from exact pairwise distances. For larger instances, we use a greedy local search and edge-coloring techniques to identify maximal sets of independent flips. Our approach ranked second overall and first in the junior category, computing provably optimal solutions for 186 out of 250 instances.