# Optimal Lower Bounds for Distributed and Streaming Spanning Forest Computation

@article{Nelson2018OptimalLB, title={Optimal Lower Bounds for Distributed and Streaming Spanning Forest Computation}, author={Jelani Nelson and Huacheng Yu}, journal={ArXiv}, year={2018}, volume={abs/1807.05135} }

We show optimal lower bounds for spanning forest computation in two different models:
* One wants a data structure for fully dynamic spanning forest in which updates can insert or delete edges amongst a base set of $n$ vertices. The sole allowed query asks for a spanning forest, which the data structure should successfully answer with some given (potentially small) constant probability $\epsilon>0$. We prove that any such data structure must use $\Omega(n\log^3 n)$ bits of memory.
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