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Twice-Ramanujan sparsifiers (2009)
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by
Joshua Batson
,
Daniel A. Spielman
,
Nikhil Srivastava
| Venue: | IN PROC. 41ST STOC |
| Citations: | 88 - 12 self |
BibTeX
@INPROCEEDINGS{Batson09twice-ramanujansparsifiers,
author = {Joshua Batson and Daniel A. Spielman and Nikhil Srivastava},
title = {Twice-Ramanujan sparsifiers},
booktitle = {IN PROC. 41ST STOC},
year = {2009},
pages = {255--262},
publisher = {}
}
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Abstract
We prove that for every d> 1 and every undirected, weighted graph G = (V, E), there exists a weighted graph H with at most ⌈d |V | ⌉ edges such that for every x ∈ IR V, 1 ≤ xT LHx x T LGx ≤ d + 1 + 2 √ d d + 1 − 2 √ d, where LG and LH are the Laplacian matrices of G and H, respectively.
