Shadoks Approach to Parallel Reconfiguration of Triangulations
This work addresses a specific computational geometry challenge for researchers and practitioners, focusing on parallel reconfiguration of triangulations, and is incremental as it builds on existing SAT and heuristic techniques.
The paper tackled the problem of finding short parallel-flip paths from multiple input triangulations to a center triangulation to minimize total path lengths, as part of the CG:SHOP 2026 Challenge, and presented a method combining SAT-based exact methods with greedy heuristics that achieved winning performance on benchmark instances.
We describe the methods used by Team Shadoks to win the CG:SHOP 2026 Challenge on parallel reconfiguration of planar triangulations. An instance is a collection of triangulations of a common point set. We must select a center triangulation and find short parallel-flip paths from each input triangulation to the center, minimizing the sum of path lengths. Our approach combines exact methods based on SAT with several greedy heuristics, and also makes use of SAT and MaxSAT for solution improvement. We present a SAT encoding for bounded-length paths and a global formulation for fixed path-length vectors. We discuss how these components interact in practice and summarize the performance of our solvers on the benchmark instances.