Annealing and Tempering for Sampling and Counting

iii ACKNOWLEDGEMENTS I would like to thank my advisors Dana Randall and Eric Vigoda for their guidance and support, which they gave generously. I was fortunate to have the opportunity to work with two of the leading researchers in my field. Dana never ceased to surprise me with her quick insights and ability to get to crux of a problem. I thoroughly enjoyed working with Eric and am always inspired by his persistent approach to solving hard problems. During my stay at Georgia Tech, I had the opportunity to interact with other faculty in theory group and the ACO program and I would like to thank them as well. I would like to thank Prasad Tetali especially, who is the nicest of people, and from whose methodical approach to research I learned a lot. I'd like to thank Vijay Vazirani for his timely advice as well as for some enjoyable discussions on problems. I'd like to thank Santosh Vempala for some fun discussions as well. Thanks to Ivona Bezáková, Juan Vera and Sam Greenberg for enjoyable discussions in the course of our collaborations. I'd like to thank all the friends I made at Georgia Tech; presence made the working environment at Tech very cordial and friendly. I would like to thank my family; my parents Rakesh and Nirupama, and my sister Melanie for their constant support and encouragement.