Algorithms and Models for Problems in Networking

Many interesting theoretical problems arise from computer networks. In this thesis we will consider three of them: algorithms and data structures for problems involving distances in networks (in particular compact routing schemes, distance labels, and distance oracles), algorithms for wireless capacity and scheduling problems, and algorithms for optimizing iBGP overlays in autonomous systems on the Internet. While at first glance these problems may seem extremely different, they are similar in that they all attempt to look at a previously studied networking problem in new, more realistic frameworks. In other words, they are all as much about new models for old problems as they are about new algorithms. In this thesis we will define these models, design algorithms for them, and prove hardness and impossibility results for these three types of problems.