Algorithmic Aspects of the Internet

ACKNOWLEDGEMENTS First, I would like to thank my advisors, Milena Mihail and Vijay Vazirani, for all I have learned from them and for sharing their insights with me which was invaluable during these four years. I also thank Dana Randall, Dick Lipton and other faculty of the ACO and College of Computing. I have also been very lucky to have wonderful colleagues and As a final note, I would like to thank my parents for their support in all these years, and to Azin for her love, support and cheerfulness. It would not be fun without her. SUMMARY The goal of this thesis is to use and advance the techniques developed in the field of exact and approximation algorithms for many of the problems arising in the context of the Internet. We will formalize the method of dual fitting and the idea of factor-revealing LP. We use this combination to design and analyze two greedy algorithms for the metric uncapacitated facility location problem. Their approximation factors are 1.861 and 1.61 respectively. We also provide the first polynomial time algorithm for the linear version of a market equilibrium model defined by Irving Fisher in 1891. Our algorithm is modeled after Kuhn's primal-dual algorithm for bipartite matching. We also study the connectivity properties of the Internet graph and its impact on its structure. In particular, we consider the model of growth with preferential attachment for modeling the graph of the Internet and prove that under some reasonable assumptions, this graph has a constant conductance.