Research Interests


My general interests are in graph theory and theoretical computer science. Recently, I have been focusing on topological graph theory, in particular embeddings of dense graphs in surfaces and problems related to the Map Color Theorem, and randomized algorithms, in particular property testing and sublinear algorithms. In the past I did some work in computer graphics and discrete geometry.


Recent Papers

Settling the genus of the n-prism
T. Sun, manuscript
Jungerman ladders and index 2 constructions for genus embeddings of dense regular graphs
T. Sun, in preparation
A Lower Bound on Cycle-Finding in Sparse Digraphs
X. Chen, T. Randolph, R. Servedio, T. Sun, SODA 2020, invited to special issue of ACM Trans. Algs.
Simultaneous constructions for minimum triangulations and complete graph embeddings
T. Sun, Ars Mathematica Contemporanea 18(20) (2020) 309-337
A simple construction for orientable triangular embeddings of the complete graphs on 12s vertices
T. Sun, Discrete Mathematics 342(4) (2019) 1147-1151   [PDF]
Face distributions of embeddings of complete graphs
T. Sun, accepted to Journal of Graph Theory   [PDF]
Sample-based high-dimensional convexity testing
X. Chen, A. Freilich, R. Servedio, T. Sun, RANDOM 2017   [full version]

Tools

Heffter-Edmonds Face Tracer
For computing the genus of a rotation system of a simple graph.

Older Work

Deployable 3D Linkages With Collision Avoidance
C. Zheng, T. Sun, X. Chen, ACM/EG SCA 2016 (Best Paper Award)
Computational Design of Twisty Joints and Puzzles
T. Sun, C. Zheng, ACM SIGGRAPH (Proc. Trans. on Graphics) 2015
Fast Multipole Representation of Diffusion Curves and Points
T. Sun, P. Thamjaroenporn, C. Zheng, ACM SIGGRAPH (Proc. Trans. on Graphics) 2014
Genus distributions of cubic series-parallel graphs
J. L. Gross, M. Kotrbčik, T. Sun, Discrete Math. and Theoretical Comp. Sci. 16(3) (2014)
On Milgram's construction and the Duke embedding conjectures
T. Sun, senior thesis, Columbia University (advisor: Jonathan L. Gross)
Drawing some 4-regular planar graphs with integer edge lengths
T. Sun, 25th Canadian Conference on Computational Geometry (2013)
Rigidity-theoretic constructions of integral Fary embeddings
T. Sun, 23rd Canadian Conference on Computational Geometry (2011)