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We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in both theory and practice, but all existing algorithms read the entire graph. In this work we design a sublinear-time algorithm for approximating the number of triangles in a graph, where the algorithm is given query access to the graph. The… (More)

We revisit the classic problem of estimating the degree distribution moments of an undirected graph. Consider an undirected graph G = (V, E) with n (non-isolated) vertices, and define (for s > 0) µ s = 1 n · v∈V d s v. Our aim is to estimate µ s within a multiplicative error of (1 + ε) (for a given approximation parameter ε > 0) in sublinear time. We… (More)

The function f : {−1, 1} n → {−1, 1} is a k-junta if it depends on at most k of its variables. We consider the problem of tolerant testing of k-juntas, where the testing algorithm must accept any function that is ǫ-close to some k-junta and reject any function that is ǫ ′-far from every k ′-junta for some ǫ ′ = O(ǫ) and k ′ = O(k). Our first result is an… (More)

This group continues its investigations of sources that generate information, channels that transmit it, and machines that process it. For sources, the main objective is to estimate the rate at which they generate information and to determine how to encode their output economically, in order to decrease the channel capacity required for transmission.… (More)

- E Arthurs, T M S Eden, P Huang, S Elias, F Asano, R M Jelinek +30 others
- 2009

Several authors have described various methods of picture coding with the object of reducing the information required to specify a picture (1-5). By using quite sophisticated schemes they succeeded in reducing the information from 6 bits/sample to 1-2 bits/sample and obtained reasonably good processed pictures. Two questions (6) were raised by their work:… (More)

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