Research Statements

Over the past two decades, I have been working on problems at the intersection of Algorithm Design, Optimization, Algorithmic Game and Economics Theories, Scientific Computation, and Parallel Processing. I am a theoretican who cares a lot about the practical impact of mathematical and algorithmic work and who appreciates interdisciplinary research. My main research interests include Smoothed Analysis of Algorithms and Heuristics, Spectral Graph Theory, Computational Game Theory, Combinatorial Scientific Computing, Combinatorial Optimization, Mathematical Programming, Parallel Scientific Computing, Graph Partitioning and Data Mining, Computational Geometry with Applications in Computer Graphics and Mesh Generation, and Graph Embedding. My secondary interests include Cryptography and Computer Security, Internet Algorithms and Software, On-Line Scheduling, Cache-Oblivious Algorithms, VLSI and Circuit Simulation, Large-scale Information Processing and Organization, Compiler Optimization, String Matching, Regression and Robust Statistics, Percolation and Phase Transition, and Bioinformatics. Although these topics above appear to be diverse, the underlying principle of my research has been the same, that is, to understand the mathematical structure of these problems in order to design efficient algorithms and software. In addition to algorithm design and analysis, I have been very active in industry participation and collaboration with engineers and scientists who develop real-world products. In the past decades, I have contributed to software products in Thinking Machine, NASA, Intel, IBM, and Akamai, including transistor-level logic simulation software, numerical simulation, internet searching, network routing and large-scale data analysis. I have received 8 patents for my work.