Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time

@article{Lee2015ConstructingLS,
  title={Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time},
  author={Y. Lee and H. Sun},
  journal={2015 IEEE 56th Annual Symposium on Foundations of Computer Science},
  year={2015},
  pages={250-269}
}
  • Y. Lee, H. Sun
  • Published 2015
  • Computer Science, Mathematics
  • 2015 IEEE 56th Annual Symposium on Foundations of Computer Science
  • We present the first almost-linear time algorithm for constructing linear-sized spectral sparsification for graphs. This improves all previous constructions of linear-sized spectral sparsification, which requires Ω(n2) time [1], [2], [3]. A key ingredient in our algorithm is a novel combination of two techniques used in literature for constructing spectral sparsification: Random sampling by effective resistance [4], and adaptive constructions based on barrier functions [1], [3]. 

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