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
Index 3 biembeddings of the complete graphs
J. F. Barajas, T. Sun, submitted
AAnim: an Animation Engine on Visualizing Algorithms and Data Structures for Educators
Z. J. Liu, T. Sun, to appear in SIGCSE TS 2023 Posters   [abstract]
Commutators in the Rubik's Cube group
T. Sun, to appear in the American Mathematical Monthly   [preprint]
On the bigenus of the complete graphs
T. Sun, Australasian Journal of Combinatorics 84(1) (2022) 212-219
Settling the genus of the n-prism
T. Sun, European Journal of Combinatorics 110 (2023) 103667
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, ACM Trans. Algs. 18(4) (2022) #31 (SODA 2020)   [conference version]
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   [preprint]
Face distributions of embeddings of complete graphs
T. Sun, Journal of Graph Theory 97(2) (2021) 281-304   [preprint]
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)