Subgraph Sparsification and Nearly Optimal Ultrasparsifiers

  title={Subgraph Sparsification and Nearly Optimal Ultrasparsifiers},
  author={Alexandra Kolla and Yury Makarychev and Amin Saberi and Shang-Hua Teng},
We consider a variation of the spectral sparsification problem where we are required to keep a subgraph of the original graph. Formally, given a union of two weighted graphs G and W and an integer k, we are asked to find a k-edge weighted graph Wk such that G+Wk is a good spectral sparsifer of G+W. We will refer to this problem as the subgraph (spectral) sparsification. We present a nontrivial condition on G and W such that a good sparsifier exists and give a polynomial-time algorithm to find… CONTINUE READING
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