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ETH Flippers Approach to Parallel Reconfiguration of Triangulations: SAT Formulation and Heuristics (CG Challenge)

Authors Lorenzo Battini , Marko Milenković

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • exact solution
  • heuristic
  • SAT solver
  • XOR clauses
  • computational geometry

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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.

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Lorenzo Battini and Marko Milenković. ETH Flippers Approach to Parallel Reconfiguration of Triangulations: SAT Formulation and Heuristics (CG Challenge). In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 105:1-105:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.105

Author Details

Lorenzo Battini
  • ETH Zürich, Switzerland
Marko Milenković
  • ETH Zürich, Switzerland

Acknowledgements

We would like to thank the Challenge organizers and other competitors for their time, feedback, and for making this whole event possible. This work was conducted as part of the Practical Work course at ETH Zürich under the supervision of Michael Hoffmann, whose guidance was invaluable. We sincerely thank Bernd Gärtner for providing travel support to attend the conference. We also acknowledge the ETH High Performance Computing group for providing the computational resources of the Euler cluster.

Supplementary Materials

References

  1. Oswin Aichholzer, Joseph Dorfer, Sándor P. Fekete, Phillip Keldenich, Peter Kramer, and Stefan Schirra. Central Triangulation under Parallel Flip Operations: The CG:SHOP Challenge 2026, 2026. URL: https://arxiv.org/abs/2603.18812.
  2. Lorenzo Battini and Marko Milenković. ETH flippers CGSHOP2026. Software, (visited on 2026-05-15). URL: https://github.com/Lbattini/ETH-flippers-CGSHOP2026
    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.26084
  3. Sabine Hanke, Thomas Ottmann, and Sven Schuierer. The edge-flipping distance of triangulations. Journal of Universal Computer Science, 2, April 1996. URL: https://doi.org/10.3217/jucs-002-08-0570.
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