CG#Hunters Approach to Central Triangulation Under Parallel Flip Operations (CG Challenge)

Lee, Jaegun; Kang, Seokyun; Lee, Hyeonseok; Yang, Hyeyun; Ahn, Taehoon

doi:10.4230/LIPIcs.SoCG.2026.108

Abstract

In the CG:SHOP 2026 Challenge, the goal is to compute a central triangulation for a given set of triangulations on the same point set while minimizing the sum of parallel flip distances. To address the problem, our team (CG#Hunters) constructs an initial solution by iteratively applying parallel flips to reduce the total number of crossings between the triangulations until none remain. To optimize these solutions, we shorten the paths by using a score-based greedy edge selection and refine the central triangulation via a large scale neighborhood search. Additionally, a representative-set-based approach is utilized to efficiently handle large instances. With these combined approaches, we achieved third place by successfully computing central triangulations with sufficiently short parallel flip paths for all 250 instances.

Cite As Get BibTex

Jaegun Lee, Seokyun Kang, Hyeonseok Lee, Hyeyun Yang, and Taehoon Ahn. CG#Hunters Approach to Central Triangulation Under Parallel Flip Operations (CG Challenge). In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 108:1-108:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.108

Author Details

Jaegun Lee

Department of Computer Science and Engineering, Pohang University of Science and Technology, Republic of Korea

Seokyun Kang

Graduate School of Artificial Intelligence, Pohang University of Science and Technology, Republic of Korea

Hyeonseok Lee

Department of Computer Science and Engineering, Ulsan National Institute of Science and Technology, Republic of Korea

Hyeyun Yang

School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Republic of Korea

Taehoon Ahn

Department of Computer Science, Sookmyung Women’s University, Seoul, Republic of Korea

Funding

Jaegun Lee, Seokyun Kang: Partly supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT) (RS-2023-00219980), and the Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. RS-2019-II191906, Artificial Intelligence Graduate School Program (POSTECH)) and (No. 2017-0-00905, Software Star Lab (Optimal Data Structure and Algorithmic Applications in Dynamic Geometric Environment)).

Lee, Hyeonseok: Supported by the Korea institute of Human Resources Development in Science and Technology (KIRD) grant funded by the Korea government (MSIT) (No. RS-2025-02215586).
Yang, Hyeyun: Supported by a KIAS Individual Grant (CG102001) at Korea Institute for Advanced Study.

Acknowledgements

We would like to thank the challenge organizers and fellow competitors for their efforts. We are also grateful to Hee-Kap Ahn and Antoine Vigneron for providing computational resources at POSTECH and UNIST, and to the Center for Advanced Computation at Korea Institute for Advanced Study for help computing resources.

Supplementary Materials

Software (Source Code) https://github.com/jagunlee/CGSHOP26.git 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.
Jérôme Galtier, Ferran Hurtado, Marc Noy, Stéphane Pérennes, and Jorge Urrutia. Simultaneous edge flipping in triangulations. International Journal of Computational Geometry & Applications, 13(02):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(8):570-579, 1996. URL: https://doi.org/10.3217/JUCS-002-08-0570.
Sariel Har-Peled and Soham Mazumdar. On coresets for k-means and k-median clustering. In Proceedings of the 36th annual ACM Symposium on Theory of Computing (STOC), pages 291-300, 2004. URL: https://doi.org/10.1145/1007352.1007400.
Ferran Hurtado, Marc Noy, and Jorge Urrutia. Flipping edges in triangulations. Discrete & Computational Geometry, 22:333-346, 1999. URL: https://doi.org/10.1007/PL00009464.
Iyad Kanj, Eric Sedgwick, and Ge Xia. Computing the flip distance between triangulations. Discrete & Computational Geometry, 58:313-344, 2017. URL: https://doi.org/10.1007/S00454-017-9867-X.
Anna Lubiw and Vinayak Pathak. Flip distance between two triangulations of a point set is NP-complete. Computational Geometry, 49:17-23, 2015. URL: https://doi.org/10.1016/J.COMGEO.2014.11.001.

CG#Hunters Approach to Central Triangulation Under Parallel Flip Operations (CG Challenge)

Authors Jaegun Lee , Seokyun Kang , Hyeonseok Lee , Hyeyun Yang , Taehoon Ahn

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