Probabilistic Algorithms for Information and Technology Flows in the Networks

This thesis studies several probabilistic algorithms for information and technology flow in large scale networks. Information flow refers to the circulation of information in social or communication networks for the purpose of disseminating or aggregating knowledge. Technology flow refers to the process in the network in which nodes incrementally adopt a certain type of technological product such as IPv6 networking protocols. In this thesis, we study the following information and technology flow problems.;First, we consider the scenario where information flow acts as media to disseminate messages. The information flow here is considered as a mechanism of replicating a piece of information from one node to another in a network with a goal to “broadcast” the knowledge to everyone. Our studies focus on a simple broadcasting algorithm that is commonly seen in mobile ad-hoc networks, namely the flooding algorithm. We give a tight characterization on the completion time of the flooding algorithm when we make natural stochastic assumptions on the availability of the communication links in the network.;Second, we consider the problem that information flow acts as a device to aggregate statistics. We interpret information flow here as artifacts produced by algorithmic procedures that serve as statistical estimators for the networks. The goal is to maintain accurate estimators with minimal information flow overhead. We study these two problems: first, we consider the continual count tracking problem in a distributed environment where the input is an aggregate stream originating from k distinct sites and the updates are allowed to be non-monotonic, i.e. both increments and decrements are allowed. By making natural stochastic assumptions over the streaming data, we develop an optimal algorithm in communication cost that can continually track the count within a prescribed relative accuracy ε. Second, we study the effectiveness of using random walks to estimate the statistical properties of networks. Specifically, we give the first general deviation bounds for random walks over possibly irreversible finite state Markov chains based on mixing time properties of the chain in both discrete and continuous time settings.;Finally, we study the problem where technology flow acts as a key to unlock innovative technology diffusion. Here, the technology flow shall be interpreted as a way to specify the circumstance, in which a node in the network will decide to adopt a new technology. Our studies focus on finding the most cost effective way to deploy networking protocols such as SecureBGP or IPv6 in the Internet. Our result is a near optimal strategy that leverages the patterns of technology flows to facilitate the new technology deployments.