Optimal Lower Bounds for Sketching Graph Cuts

@article{Carlson2019OptimalLB,
  title={Optimal Lower Bounds for Sketching Graph Cuts},
  author={Charles Carlson and Alexandra Kolla and Nikhil Srivastava and Luca Trevisan},
  journal={ArXiv},
  year={2019},
  volume={abs/1712.10261}
}
We study the space complexity of sketching cuts and Laplacian quadratic forms of graphs. We show that any data structure which approximately stores the sizes of all cuts in an undirected graph on $n$ vertices up to a $1+\epsilon$ error must use $\Omega(n\log n/\epsilon^2)$ bits of space in the worst case, improving the $\Omega(n/\epsilon^2)$ bound of Andoni et al. and matching the best known upper bound achieved by spectral sparsifiers. Our proof is based on a rigidity phenomenon for cut (and… 
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