Shadoks Approach to Parallel Reconfiguration of Triangulations

2026-03-22

AI Summary

This work addresses the problem of parallel reconfiguration among multiple triangulations by selecting a central triangulation and computing short parallel flip sequences from each input triangulation to this center, with the objective of minimizing the total path length. To achieve this, the authors introduce a novel integration of SAT and MaxSAT solvers, proposing a specialized SAT encoding for bounded-length flip paths and a global optimization model for fixed path-length vectors. A greedy heuristic is further incorporated to accelerate the solution process. The method demonstrates outstanding performance on the CG:SHOP 2026 challenge benchmarks, securing first place by significantly improving both computational efficiency and solution quality.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• parallel reconfiguration
• triangulations
• flip paths
• center triangulation
• path length minimization

Innovation

• parallel reconfiguration
• triangulations
• SAT encoding
• MaxSAT
• bounded-length paths