Shadoks Approach to Parallel Reconfiguration of Triangulations

TL;DR

This paper details Team Shadoks' winning strategy in the CG:SHOP 2026 Challenge, combining SAT-based exact methods and heuristics to efficiently reconfigure planar triangulations in parallel.

Contribution

It introduces a novel combination of SAT encoding, heuristics, and MaxSAT techniques for optimizing parallel reconfiguration of triangulations.

Findings

SAT encoding effectively models bounded-length paths

Heuristic methods improve solution quality

Solver performance is competitive on benchmark instances

Abstract

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.