Distributed anonymous discrete function computation

We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes. In this model, each node has bounded computation and storage capabilities that do not grow with the network size. Furthermore, each node only knows its neighbors, not the entire graph. Our goal is to characterize the class of functions that can be computed within this model. In our main result, we provide a necessary condition for computability which we show to be nearly sufficient, in the sense that every function that satisfies this condition can at least be approximated. The problem of computing suitably rounded averages in a distributed manner plays a central role in our development; we provide an algorithm that solves it in time that grows quadratically with the size of the network

Efficient Information Aggregation Strategies for Distributed Control and Signal Processing

This thesis is concerned with distributed control and coordination of networks consisting of multiple, potentially mobile, agents. This is motivated mainly by the emergence of large scale networks characterized by the lack of centralized access to information and time-varying connectivity. Control and optimization algorithms deployed in such networks should be completely distributed, relying only on local observations and information, and robust against unexpected changes in topology such as link failures. We will describe protocols to solve certain control and signal processing problems in this setting. We will demonstrate that a key challenge for such systems is the problem of computing averages in a decentralized way. Namely, we will show that a number of distributed control and signal processing problems can be solved straightforwardly if solutions to the averaging problem are available. The rest of the thesis will be concerned with algorithms for the averaging problem and its generalizations. We will (i) derive the fastest known averaging algorithms in a variety of settings and subject to a variety of communication and storage constraints (ii) prove a lower bound identifying a fundamental barrier for averaging algorithms (iii) propose a new model for distributed function computation which reflects the constraints facing many large-scale networks, and nearly characterize the general class of functions which can be computed in this model.Comment: Ph.D. thesis, Department of Electrical Engineering and Computer Science, MIT, September 201