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Distributed Anonymous Discrete Function Computation

Authors :: Alex Olshevsky
John N. Tsitsiklis
Julien M. Hendrickx
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Tsitsiklis, John N.
Hendrickx, Julien
Olshevsky, Alexander
Source :: arXiv
Publication Year :: 2011
Publisher :: Institute of Electrical and Electronics Engineers (IEEE), 2011.
Abstract: 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 violates 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.<br />National Science Foundation (U.S.) (Graduate Fellowship)<br />National Science Foundation (U.S.) (Grant ECCS-0701623)<br />Belgian American Educational Foundation, inc. (Postdoctoral Fellowship)<br />Belgian National Foundation for Scientific Research (Postdoctoral Fellowship)