Approximately Counting Subgraphs in Data Streams

Estimating the number of subgraphs in data streams is a fundamental problem that has received great attention in the past decade. In this paper, we give improved streaming algorithms for approximately counting the number of occurrences of an arbitrary subgraph H , denoted #H , when the input graph G is represented as a stream of.. edges. To obtain our algorithms, we provide a generic transformation that converts constant-round sublinear-time graph algorithms in the query access model to constant-pass sublinear-space graph streaming algorithms. Using this transformation, we obtain the following results. center dot We give a 3-pass turnstile streaming algorithm for (1 +/- epsilon) - approximating #H in (Omicron) over tilde (m(rho(H))/ epsilon(2) center dot #H) space, where rho(H) is the fractional edge-cover of... This improves upon and generalizes a result of McGregor et al. [PODS 2016], who gave a 3-pass insertion-only streaming algorithm for ( 1 +/- c)- approximating the number #T of triangles in (Omicron) over tilde (m(3/2)/epsilon(2) center dot #T ) space if the algorithm is given additional oracle access to the degrees. center dot We provide a constant-pass streaming algorithm for (1 +/- epsilon)- approximating #K-r in (Omicron) over tilde (m lambda(r-2)/ epsilon(2) center dot#K-r) space for any r >= 3, in a graph G with degeneracy lambda, where K-r is a clique on r vertices. This resolves a conjecture by Bera and Seshadhri [PODS 2020]. More generally, our reduction relates the adaptivity of a query algorithm to the pass complexity of a corresponding streaming algorithm, and it is applicable to all algorithms in standard sublinear-time graph query models, e.g., the (augmented) general model.