Streaming Algorithms for Approximating the Number of $H$-Subgraphs

From Open Problems in Sublinear Algorithms
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Suggested by He Sun
Source Warwick 2018

Designing a streaming algorithm that approximately computes the number of a subgraph is an intensively studied problem with applications in data mining and database theory. The space complexities of such algorithms are usually a function of $\#$H (the number of subgraph $H$), so an algorithm gives a good approximation of $\#H$ in sublinear space only if a reasonable lower bound of $\#H$ is known in advance, which is not realistic for some scenarios. It’s practically interesting to study the possibility of designing a multi-pass streaming algorithm which gives a guaranteed approximation of $\#H$ and does not assume the knowledge of a lower bound of $\#H$. Specifically, it is interesting to see, for any algorithm that gives an $\alpha$-approximation of $\#H$, the relationship needed among $\alpha$, the space complexity and the number of passes (not necessarily a constant) that the algorithm needs to read the input graph stream.