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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)

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)

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)

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