### 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 language | English (US) |
---|---|

Pages (from-to) | 1805-1822 |

Number of pages | 18 |

Journal | Linear and Multilinear Algebra |

Volume | 65 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2 2017 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Linear and Multilinear Algebra*,

*65*(9), 1805-1822. https://doi.org/10.1080/03081087.2016.1256944

}

*Linear and Multilinear Algebra*, vol. 65, no. 9, pp. 1805-1822. https://doi.org/10.1080/03081087.2016.1256944

**On the approximation of Laplacian eigenvalues in graph disaggregation.** / Hu, Xiaozhe; Urschel, John Cameron; Zikatanov, Ludmil Tomov.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the approximation of Laplacian eigenvalues in graph disaggregation

AU - Hu, Xiaozhe

AU - Urschel, John Cameron

AU - Zikatanov, Ludmil Tomov

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.

UR - http://www.scopus.com/inward/record.url?scp=84994806250&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994806250&partnerID=8YFLogxK

U2 - 10.1080/03081087.2016.1256944

DO - 10.1080/03081087.2016.1256944

M3 - Article

VL - 65

SP - 1805

EP - 1822

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 9

ER -