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I sincerely thank my advisor Dr. Shashi Shekhar for guiding and providing ideas throughout this project. I take this opportunity to thank Dr. Shashi Shekhar for letting me work with his group and guide me throughout my graduate studies. I thank Dr. Bradley Carlin and Dr. Jaideep Srivastava for agreeing to participate in my project defense. I thank James Kang, and Mete Celik for collaborating with me on the research papers that were published out of this project. I thank Spatial Database group at the University of Minnesota for their help in my research work and providing feedback to improve my presentation. I also thank Dr. Junchang Ju, Dr. Sucharita Gopal, and Dr. Eric Kolaczyk at the Boston University for introducing me to the application domain. A special thanks to Kim Koffolt for improving the readability of my research papers. Most of all, I dedicate my graduate degree to my mother, Neeta Gandhi, for her selfless love and support through-out my life. Without her support, I couldn’t have come so far. I am proud to have my brother, Jay Gandhi, and friend Naveen Nagarajan, whom I can always rely on for help and encouragement. 2 Many statistical queries such as maximum likelihood estimation involve finding the best candidate model give