# Dynamic Streaming Spectral Sparsification in Nearly Linear Time and Space

@article{Kapralov2019DynamicSS,
title={Dynamic Streaming Spectral Sparsification in Nearly Linear Time and Space},
author={Mikhail Kapralov and Navid Nouri and Aaron Sidford and Jakab Tardos},
journal={ArXiv},
year={2019},
volume={abs/1903.12150}
}
In this paper we consider the problem of computing spectral approximations to graphs in the single pass dynamic streaming model. We provide a linear sketching based solution that given a stream of edge insertions and deletions to a $n$-node undirected graph, uses $\tilde O(n)$ space, processes each update in $\tilde O(1)$ time, and with high probability recovers a spectral sparsifier in $\tilde O(n)$ time. Prior to our work, state of the art results either used near optimal $\tilde O(n)$ space… CONTINUE READING
3