Towards scalable spectral sparsification of directed graphs
Document Type
Conference Proceeding
Publication Date
8-2019
Department
Department of Electrical and Computer Engineering
Abstract
Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the the first few eigenvalues and eigenvectors of the graph Laplacian, leading to the development of a variety of nearly-linear time numerical and graph algorithms. However, there is not a unified approach that allows for truly-scalable spectral sparsification of both directed and undirected graphs. For the first time, we prove the existence of linear-sized spectral sparsifiers for general directed graphs, and introduce a practically-efficient yet unified spectral graph sparsification approach that allows sparsifying real-world, large-scale directed and undirected graphs with guaranteed preservation of the original graph spectra. By exploiting a highly-scalable (nearly-linear complexity) spectral matrix perturbation analysis framework for constructing nearly-linear sized (directed) subgraphs, it enables to well preserve the key eigenvalues and eigenvectors of the original (directed) graph Laplacians.
Publication Title
2019 IEEE International Conference on Embedded Software and Systems (ICESS)
Recommended Citation
Zhang, Y.,
Zhao, Z.,
&
Feng, Z.
(2019).
Towards scalable spectral sparsification of directed graphs.
2019 IEEE International Conference on Embedded Software and Systems (ICESS).
http://doi.org/10.1109/ICESS.2019.8782449
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/911
Publisher's Statement
©2019 IEEE. Publisher’s version of record: https://doi.org/10.1109/ICESS.2019.8782449