Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
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Networks are becoming increasingly prominent as a framework for understanding designed or natural phenomena, ranging from decentralized computer systems to social interaction patterns. They serve as a means to facilitate decentralized computation and the dissemination of information. Designing and analyzing their function therefore requires a theory of information flow in networks. The goal of such a theory is to help in developing algorithms for core questions, including: How to find a piece of information? How to spread information? How to perform shared computations? In this thesis, we explore several facets of these problems. We propose a graph-based model termed temporal networks, which captures in a precise way the information flow dynamics of a history of communications in a network. Building on this methodology, we analyze a simple random distribution called Spatial Gossip, which disseminates information fast both locally and globally. Building in turn on Spatial Gossip, we design and analyze simple protocols for several locality-based problems, including the Resource Location Problem, in which nodes are trying to locate the closest copy of some desirable resource in the network. In all of the above protocols, we wish to restrict the sizes of messages, as communication bandwidth is often a scarce resource. We study the impact of message size more thoroughly, by exhibiting connections between the random distributions that are used for gossip, and the problems that can be solved with small messages. In particular, we show that uniform gossip cannot solve any of the above locality-based problems fast and with small messages. We take the study of message sizes further by proposing and analyzing simple gossip-based protocols for computing sums, averages, random samples, quantiles, and other aggregate functions of data that is distributed over the nodes of a network. Finally, we look at decentralized communication as it occurs in the diffusion of information, or innovations, in social networks. We give a constant-factor approximation for the problem of using a given budget to maximize the expected spread of an innovation or product through a network, by choosing suitable target nodes or marketing actions.