\chapter*{Acknowledgements}
It is with great encouragements and help from my advisor, teachers, friends and family
that I have been able to accomplish the work in this dissertation. 


First and formost, I wish to express my gratitude to my advisor, Professor Qi Cheng.
I learned so much from him through discussions during classes, meetings, and lunch hours.
His critical and creative instruction has cultivated my approach to research. 
His passion and determination has encouraged me to explore and work.
His optimism and humour has affected me to enjoy work and life.
His guidance and support has helped me to persist during all these years.
He has been a fantastic professor, advisor and friend. 
I am grateful for having had the opportunity to work with him.


I also wish to thank my dissertation committee members: Professors Sudarshan Dhall, Changwook Kim,
Ralf Schmidt, and Krishnaiyan Thulasiraman. They have given me valuable suggestions and comments
in the general exam and during the revision of this dissertation. My thanks also go to the other faculty and staff
in the school of computer science at OU. In addition, I would like to thank all my teachers and mentors along these years.

Parts of Chapter 3 are from joint work with Prof. Qi Cheng and Dr. Jiyou Li and previously appeared in \cite{CLZ13}.
Parts of Chapter 4 are from joint work with Prof. Qi Cheng and Prof. Daqing Wan and previously appeared in \cite{CWZ13}.
It has been a pleasure to work with them. I want to thank them for helpful discussions.
I would like to thank professor E. Thom{\'e}  for informing me of the update of their paper. 
I want to thank my friends for their help during my graduate research. 
I also want to thank the staff in the OU Writing Center for the suggestions concerning 
the revision of this dissertation. Some experiments have been performed using Sage and PARI,
I want to thank the developers of these software.

Last but not least, I am grateful to my family for their lasting love and support.
In particular, I want to thank my grandparents, my parents and my sister.
