Graph Sparsification by Effective Resistances

@inproceedings{Spielman2008GraphSB,
  title={Graph Sparsification by Effective Resistances},
  author={Daniel A. Spielman and Nikhil Srivastava},
  booktitle={STOC},
  year={2008}
}
We present a nearly-linear time algorithm that produces high-quality sparsifiers of weighted graphs. Given as input a weighted graph G=(V,E,w) and a parameter ε>0, we produce a weighted subgraph H=(V,~E,~w) of G such that |~E|=O(n log n/ε<sup>2</sup>) and for all vectors x in R<sup>V</sup>. (1-ε) ∑uv ∈ E (x(u)-x(v))<sup>2</sup>w<sub>uv</sub>≤ ∑uv in ~E(x(u)-x(v))<sup>2</sup>~w<sub>uv</sub> ≤ (1+ε)∑uv ∈ E(x(u)-x(v))<sup>2</sup>w<sub>uv</sub>. This improves upon the sparsifiers constructed by… CONTINUE READING
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