Author(s)Bodas, Shreeshankar; Shah, Devavrat
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We are interested in the following question: given n numbers x[subscript 1], ..., x[subscript n], what sorts of approximation of average x[subscript ave] = 1overn (x[subscript 1] + ... + x[subscript n]) can be achieved by knowing only r of these n numbers. Indeed the answer depends on the variation in these n numbers. As the main result, we show that if the vector of these n numbers satisfies certain regularity properties captured in the form of finiteness of their empirical moments (third or higher), then it is possible to compute approximation of x[subscript ave] that is within 1 ±ε multiplicative factor with probability at least 1 - δ by choosing, on an average, r = r(ε, δ, σ) of the n numbers at random with r is dependent only on ε, δ and the amount of variation σ in the vector and is independent of n. The task of computing average has a variety of applications such as distributed estimation and optimization, a model for reaching consensus and computing symmetric functions. We discuss implications of the result in the context of two applications: load-balancing in a computational facility running MapReduce, and fast distributed averaging.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
IEEE International Symposium on Information Theory Proceedings 2011 (ISIT)
Institute of Electrical and Electronics Engineers (IEEE)
Bodas, Shreeshankar, and Devavrat Shah. “Fast Averaging.” IEEE International Symposium on Information Theory Proceedings 2011 (ISIT). 2153–2157.
Author's final manuscript