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Incremental Algorithm and Local Search for Minimum Non-Obtuse Triangulations (CG Challenge)

Authors Taehoon Ahn , Jaegun Lee , Byeonguk Kang , Hwi Kim

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Triangulation
  • Non-obtuse triangle
  • Steiner point
  • Incremental algorithm
  • Local search

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Abstract

In this year’s CG challenge, the task was to compute a non-obtuse triangulation of given planar regions while minimizing the number of Steiner points. Our team (Gwamegi) used two approaches. The first approach incrementally adds Steiner points on the grid defined by the input points in the planar regions, while maintaining a Delaunay triangulation. The second approach is an iterated local search, which runs insertion and deletion steps alternatingly. In the insertion step, we add a new Steiner point inside a maximal convex subpolygon in the current triangulation. In the deletion step, we remove a number of Steiner points packed in a small region. We use both our approaches to obtain non-obtuse triangulations for all 150 instances. We use our second approach to reduce the number of Steiner points from the non-obtuse triangulations. We have successfully computed non-obtuse triangulations using a sufficiently small number of Steiner points for all instances.

Cite As Get BibTex

Taehoon Ahn, Jaegun Lee, Byeonguk Kang, and Hwi Kim. Incremental Algorithm and Local Search for Minimum Non-Obtuse Triangulations (CG Challenge). In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 80:1-80:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.80

Author Details

Taehoon Ahn
  • National Institute for Mathematical Sciences, Daejeon, South Korea
Jaegun Lee
  • Department of Computer Science and Engineering, Pohang University of Science and Technology, Pohang, Korea
Byeonguk Kang
  • Department of Computer Science and Engineering, Pohang University of Science and Technology, Pohang, Korea
Hwi Kim
  • Department of Computer Science and Engineering, Pohang University of Science and Technology, Pohang, Korea

Funding

Taehoon Ahn was supported by the National Institute for Mathematical Sciences (NIMS) grant funded by the Korea government (MSIT) (No. NIMS-B25910000). Jaegun Lee, Byeonguk Kang, and Hwi Kim were supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2023-00219980).

Acknowledgements

We would like to thank the challenge organizers and other competitors for their effort on the event. We would also like to thank Hee-Kap Ahn for providing the computational resources of the Algorithms laboratory of POSTECH.

Supplementary Materials

References

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