- Heuna Kim, Günter Rote, Congruence Testing for Point Sets in 4-space, 32nd International Symposium on Computational Geometry (SoCG 2016).
- Tools & Keywords: Coxeter classification, Grassmannian, Plücker embedding, Hopf fibrations, Kissing Number, Symmetry Groups, Rotations, Shape Matching, Real-RAM Model, Computational Geometry.
- Whether the curse of dimensionality can be overcome for congruence testing is a well-known long-standing open problem in computational geometry. This research contributes to this problem by creating an optimal algorithm in 4-space.

- Michael G. Dobbins, Heuna Kim, Luis Montejano, and Edgardo Roldan-Pensado, Shadows of a Closed Curve, soon in Arxiv.
- Prosenjit Bose, Jean-Lou De Carufel, Michael G. Dobbins, Heuna Kim, and Giovanni Viglietta, The Shadows of a Cycle Cannot All Be Paths, In Proceedings of the 27th Canadian Conference on Computational Geometry (CCCG'15), pp. 70-75, 2015.
- Tools & Keywords: Tomography, Fixed points, Orthogonal Projections, Topology, Oskar's Maze.
- This research is motivated by a 3-dimensional puzzle which asks how to embed a closed curve so that three of its orthogonal projections (shadows) become all trees. It is shown that (1) there exists no closed curve whose more than two of whose shadows are paths, (2) a d-sphere all of whose shadows are contractible can be constructed in (d+2)-space, and (3) a path can be embedded in 3-space so that all of its shadows are closed curves.

- Heuna Kim, Till Miltzow. Packing Segments in a Simple Polygon is APX-hard, In Abstracts of the 31st European Workshop on Computational Geometry (EuroCG), 2015.
- Michael Gene Dobbins and Heuna Kim. Packing Segments in a Convex 3-Polytope is NP-hard, In Abstracts of the 30th European Workshop on Computational Geometry (EuroCG), 2014.
- Tools & Keywords: NP-hard, APX-hard, Approximation Algorithms, Line Segment, Packing, Kakeya's Problem, Convex 3-polytopes, Simple Polygons.
- Packing the maximum number of line segments in a container is one of fundamental geometric packing problems. The research results include (1) APX-hardness when a container is a simple polygon, (2) NP-hardness when a container is a convex 3-polytope, and (3) an approximation algorithm when a container is a convex polygon.

- Heuna Kim, Wolfgang Mulzer, and Eunjin Oh. The Number of Combinatorially Different Convex Hulls of Points in Lines, In Abstracts of the 31st European Workshop on Computational Geometry (EuroCG), 2015.
- Tools & Keywords: Imprecise data, Zone Theorem, Line Arrangements, Convex hulls, Order Types, Ruling Surfaces.
- For a given line arrangement, exactly one point is chosen from each line segment; the convex hull of this set of points can be represented by a cyclic sequence of line labels. This research shows an upper bound and a lower bound of the number of such possible cyclic sequences. Further research on a better bound, enumeration algorithms, and higher-dimensional algorithms is in progress.

- Otfried Cheong, Sariel Har-Peled, Heuna Kim, and Hyo-Sil Kim. On the number of edges of a fan-crossing free graph, Algorithmica, 73 (2015) 673--695. (On invitation, special issue on ISAAC 2013.)
- Tools & Keywords: Fan-crossing Graphs, Quasi-planar Graphs, Graph Drawing/Embedding.
- A fan-crossing is a triple of edges such that two of them share a vertex and another crosses these two edges. This paper shows the tight bound of the maximum number of edges in fan-crossing free graphs by using combinatorial arguments.

- Hyejin Park, Heun A Kim, Seung-ho Yang, and Jaewook Lee, Transductive Bayesian regression via manifold learning of prior data structure, Expert Systems with Applications, Vol.39, No.16, pp.12557-12563, 2012
- Tools & Keywords: Manifold Learning, Dimension Reduction, LTSA (Local Tangent Space Alignment), Regression, Baysian, Transductive Process.
- To provide efficient and robust regression methods, an inductive process of one of manifold learning techniques is derived together with its implementation.