Convergence Speed in Distributed Consensus and Averaging

We propose three new algorithms for the distributed averaging and consensus problems: two for the fixed-graph case, and one for the dynamic-topology case. The convergence times of our fixed-graph algorithms compare favorably with other known methods, while our algorithm for the dynamic-topology case is the first to be accompanied by a polynomial-time bound on the worst-case convergence time. Thesis Supervisor: John N. Tsitsiklis Title: Professor Acknowledgments I am grateful to my advisor, John Tsitsiklis, for his invaluable guidance and tireless efforts in supervising this thesis. I have greatly benefitted from his help, suggestions, insight, and patience. I want to thank Prof. Vincent Blondel and Prof. Ali Jadbabaie for useful conversations that have helped me in the course of my research. I want to thank Mukul Agarwal, Constantine Caramanis, and Aman Chawla. I have learned much from my conversations with them. I thank my parents for all the encouragement they have given me over the years. Finally, I want to thank Angela for her constant support. This research was supported by the National Science Foundation under a Graduate Research Fellowship and grant ECS-0312921.