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- W1878170478 abstract "Spectral graph sparsification has emerged as a powerful tool in the analysis of large-scale networks by reducing the overall number of edges, while maintaining a comparable graph Laplacian matrix. In this paper, we present an efficient algorithm for the construction of a new type of spectral sparsifier, the unweighted spectral sparsifier. Given a general undirected and unweighted graph $G = (V, E)$ and an integer $ell < |E|$ (the number of edges in $E$), we compute an unweighted graph $H = (V, F)$ with $F subset E$ and $|F| = ell$ such that for every $x in mathbb{R}^{V}$ [ {displaystyle frac{x^T L_G x}{kappa} leq x^T L_H x leq x^T L_G x,} ] where $L_G$ and $L_H$ are the Laplacian matrices for $G$ and $H$, respectively, and $kappa geq 1$ is a slowly-varying function of $|V|, |E|$ and $ell$. This work addresses the open question of the existence of unweighted graph sparsifiers for unweighted graphs. Additionally, our algorithm can efficiently compute unweighted graph sparsifiers for weighted graphs, leading to sparsified graphs that retain the weights of the original graphs." @default.
- W1878170478 created "2016-06-24" @default.
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- W1878170478 date "2014-10-16" @default.
- W1878170478 modified "2023-09-27" @default.
- W1878170478 title "An Efficient Algorithm for Unweighted Spectral Graph Sparsification" @default.
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