TY - JOUR

T1 - On the approximation of Laplacian eigenvalues in graph disaggregation

AU - Hu, Xiaozhe

AU - Urschel, John C.

AU - Zikatanov, Ludmil T.

N1 - Funding Information:
The work of Ludmil Zikatanov was supported in part by the National Science Foundation [grant number DMS-1418843] and [grant number DMS-1522615]. Ludmil Zikatanov also supported for this work from the Department of Mathematics at Tufts University.
Publisher Copyright:
© 2016 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2017/9/2

Y1 - 2017/9/2

N2 - Graph disaggregation is a technique used to address the high cost of computation for power law graphs on parallel processors. The few high-degree vertices are broken into multiple small-degree vertices, in order to allow for more efficient computation in parallel. In particular, we consider computations involving the graph Laplacian, which has significant applications, including diffusion mapping and graph partitioning, among others. We prove results regarding the spectral approximation of the Laplacian of the original graph by the Laplacian of the disaggregated graph. In addition, we construct an alternate disaggregation operator whose eigenvalues interlace those of the original Laplacian. Using this alternate operator, we construct a uniform preconditioner for the original graph Laplacian.

AB - Graph disaggregation is a technique used to address the high cost of computation for power law graphs on parallel processors. The few high-degree vertices are broken into multiple small-degree vertices, in order to allow for more efficient computation in parallel. In particular, we consider computations involving the graph Laplacian, which has significant applications, including diffusion mapping and graph partitioning, among others. We prove results regarding the spectral approximation of the Laplacian of the original graph by the Laplacian of the disaggregated graph. In addition, we construct an alternate disaggregation operator whose eigenvalues interlace those of the original Laplacian. Using this alternate operator, we construct a uniform preconditioner for the original graph Laplacian.

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U2 - 10.1080/03081087.2016.1256944

DO - 10.1080/03081087.2016.1256944

M3 - Article

AN - SCOPUS:84994806250

SN - 0308-1087

VL - 65

SP - 1805

EP - 1822

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 9

ER -