Engineering Greedy Heuristics and Simulated Annealing Methods for the Median Triangulation Under the Parallel Flip Distance (CG Challenge)

Conradi, Jacobus; Kolbe, Benedikt; Mayer, Philip; Sauer, Jonas; Spalding-Jamieson, Jack

doi:10.4230/LIPIcs.SoCG.2026.106

Abstract

We present our approach for the CG:SHOP 2026 challenge. In this international challenge, the goal was to find a median triangulation for a set of triangulations in the parallel flip reconfiguration graph of all triangulations of an underlying point set. Our simulated-annealing-based approach makes use of two ingredients: a heuristic edge selection for approximating the parallel flip distance of two given triangulations, and a heuristic procedure to generate good initial triangulations.

Cite As Get BibTex

Jacobus Conradi, Benedikt Kolbe, Philip Mayer, Jonas Sauer, and Jack Spalding-Jamieson. Engineering Greedy Heuristics and Simulated Annealing Methods for the Median Triangulation Under the Parallel Flip Distance (CG Challenge). In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 106:1-106:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.106

Author Details

Jacobus Conradi

BARC, University of Copenhagen, Denmark

Benedikt Kolbe

Hausdorff Center for Mathematics, University of Bonn, Germany

Philip Mayer

Institute of Computer Science, University of Bonn, Germany

Jonas Sauer

Karlsruhe Institute of Technology, Germany

Jack Spalding-Jamieson

Independent, Vancouver, Canada

Funding

Conradi, Jacobus: Supported by the Carlsberg Foundation, grant CF24-1929.
Kolbe, Benedikt: This work was partially supported by the Lamarr Institute for Machine Learning and Artificial Intelligence.
Mayer, Philip: Supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant FOR-5361 - 459420781.
Sauer, Jonas: Supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant FOR-5361 - 459420781.

Acknowledgements

We thank the challenge organizers and other competitors for their time, feedback, and for making this competition and this research possible. We gratefully acknowledge access to the Marvin cluster of the University of Bonn.

Supplementary Materials

Software (Source Code) https://github.com/PhilipMayer94/jflip browse archived version

References

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.
Jon L. Bentley and Thomas A. Ottmann. Algorithms for reporting and counting geometric intersections. IEEE Transactions on Computers, C-28(9):643-647, 1979. URL: https://doi.org/10.1109/TC.1979.1675432.
Guilherme Dias da Fonseca and Yan Gerard. Shadoks approach to parallel reconfiguration of triangulations. In Proceedings of the Symposium on Computational Geometry (SoCG), 2026. URL: https://doi.org/10.4230/LIPIcs.SoCG.2026.107.
Jérôme Galtier, Ferran Hurtado, Marc Noy, Stephane Perennes, and Jorge Urrutia. Simultaneous edge flipping in triangulations. Int. J. Comput. Geom. Appl., 13(2):113-133, 2003. URL: https://doi.org/10.1142/S0218195903001098.
Sabine Hanke, Thomas Ottmann, and Sven Schuierer. The edge-flipping distance of triangulations. Journal of Universal Computer Science, 2:570-579, April 1996. URL: https://doi.org/10.3217/JUCS-002-08-0570.
S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science, 220(4598):671-680, 1983. URL: https://doi.org/10.1126/science.220.4598.671.
Charles L. Lawson. Transforming triangulations. Discrete Mathematics, 3(4):365-372, 1972. URL: https://doi.org/10.1016/0012-365X(72)90093-3.
Anna Lubiw and Vinayak Pathak. Flip distance between two triangulations of a point set is NP-complete. Computational Geometry, 49:17-23, 2015. 24th Canadian Conference on Computational Geometry (CCCG'12). URL: https://doi.org/10.1016/j.comgeo.2014.11.001.
Philip Mayer and Petra Mutzel. Engineering A* Search for the Flip Distance of Plane Triangulations. In 22nd International Symposium on Experimental Algorithms (SEA 2024), volume 301 of Leibniz International Proceedings in Informatics (LIPIcs), pages 23:1-23:20, Dagstuhl, Germany, 2024. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.SEA.2024.23.
Alexander Pilz. Flip distance between triangulations of a planar point set is APX-hard. Computational Geometry, 47(5):589-604, 2014. URL: https://doi.org/10.1016/j.comgeo.2014.01.001.

Engineering Greedy Heuristics and Simulated Annealing Methods for the Median Triangulation Under the Parallel Flip Distance (CG Challenge)

Authors Jacobus Conradi , Benedikt Kolbe , Philip Mayer , Jonas Sauer , Jack Spalding-Jamieson

File

Document Identifiers

Subject Classification

ACM Subject Classification

Keywords

Metrics

Abstract

Cite As Get BibTex

Author Details

Acknowledgements

References

Thanks for your feedback!

Could not send message