Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time
Yin Tat Leea b, He Sunc d
- aDepartment of Mathematics, MIT, Cambridge, USA
- bDept. of Math., MIT, Cambridge, MA, USA#TAB#
- cDepartment of Computer Science, University of Bristol, Bristol, UK
- dDepartment of Computer Science University of Bristol Bristol UK
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Abstract
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].
TL;DRThis work presents the first almost-linear time algorithm for constructing linear-sized spectral sparsification for graphs, using a novel combination of two techniques used in literature for constructing spectralSparsification: Random sampling by effective resistance and adaptive constructions based on barrier functions. (Semantic Scholar)