On the approximation of Laplacian eigenvalues in graph disaggregation

Xiaozhe Hu, John Cameron Urschel, Ludmil Tomov Zikatanov

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1805-1822
Number of pages18
JournalLinear and Multilinear Algebra
Volume65
Issue number9
DOIs
StatePublished - Sep 2 2017

Fingerprint

Laplacian Eigenvalues
Disaggregation
Graph Laplacian
Vertex Degree
Approximation
Graph in graph theory
Alternate
Spectral Approximation
Graph Partitioning
Parallel Processors
Operator
Preconditioner
Power Law
Eigenvalue
Costs

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Hu, Xiaozhe ; Urschel, John Cameron ; Zikatanov, Ludmil Tomov. / On the approximation of Laplacian eigenvalues in graph disaggregation. In: Linear and Multilinear Algebra. 2017 ; Vol. 65, No. 9. pp. 1805-1822.
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On the approximation of Laplacian eigenvalues in graph disaggregation. / Hu, Xiaozhe; Urschel, John Cameron; Zikatanov, Ludmil Tomov.

In: Linear and Multilinear Algebra, Vol. 65, No. 9, 02.09.2017, p. 1805-1822.

Research output: Contribution to journalArticle

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