Zhihan Gao began Ph.D. studies in C&O in September 2011, after completing a Master's degree at Nankai University (China). He completed his Ph.D. in July 2015. His thesis, entitled Approximaton Algorithms for Path TSP, ATSP and TAP via Relaxations, was supervised by Professor Joseph Cheriyan.
Zhihan's research interests are in Approximation Algorithms, a topic that lies in the intersection of Combinatorial Optimization and Theoretical Computer Science. The major contributions in his outstanding Ph.D. thesis were the following:
- A beautiful and stunningly simple 3⁄2-approximation algorithm for the graphic s-t path Traveling Salesman Problem (TSP).
- The introduction of the notion of a "unified correction vector" and its application to the design and analysis of approximation algorithms for the metric s-t path TSP. The new algorithms are substantially simpler than the previous algorithms by An, Kleinberg and Shmoys (2012) and Sebö (2013), and are based on powerful and versatile new techniques.
- Lower bounds on the integrality ratio of the Sherali-Adams relaxation of the Asymmetric Traveling Salesman Problem (ATSP).
- An elaborate framework for Lasserre lift-and-project systems that was used to design a (3⁄2 + ε)-approximation algorithm for the Tree Augmentation Problem (see Part I and Part II), thereby resolving an important problem that had been open for several years.
The problems that Zhihan tackled in his Ph.D. thesis are fundamental in the field of combinatorial optimization. His results have been praised by numerous experts, and have already been taught to graduate students around the world. Zhihan's work was presented at top-tier theoretical computer science conferences APPROX and ICALP, and published in leading journals such as Mathematical Programming, SIAM Journal on Discrete Mathematics, Operations Research Letters, and Algorithmica.
Zhihan is presently doing a postdoctoral fellowship in the Department of Statistics and Actuarial Sciences at the University of Waterloo. He is working on applications of optimization in finance and insurance.