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Title: Multilevel graph embedding

Abstract

The goal of the present paper is the design of embeddings of a general sparse graph into a set of points in $$\mathbb{R}^d$$ for appropriate d ≥ 2. The embeddings that we are looking at here aim to keep vertices that are grouped in communities together and keep the rest apart. To achieve this property, we utilize coarsening that respects possible community structures of the given graph. We employ a hierarchical multilevel coarsening approach that identifies communities (strongly connected groups of vertices) at every level. The multilevel strategy allows any given (presumably expensive) graph embedding algorithm to be made into a more scalable (and faster) algorithm. We demonstrate the presented approach on a number of given embedding algorithms and large-scale graphs and achieve speed-up over the methods in a recent paper.

Authors:
ORCiD logo [1];  [2]
  1. Northeastern Univ., Boston, MA (United States). Computer Science Dept.
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Portland State Univ., OR (United States). Dept. of Mathematics and Statistics
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1669230
Report Number(s):
LLNL-JRNL-777449
Journal ID: ISSN 1070-5325; 971424
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Numerical Linear Algebra with Applications
Additional Journal Information:
Journal Name: Numerical Linear Algebra with Applications; Journal ID: ISSN 1070-5325
Publisher:
Wiley
Country of Publication:
United States
Language:
English

Citation Formats

Quiring, Benjamin, and Vassilevski, Panayot S. Multilevel graph embedding. United States: N. p., 2020. Web. doi:10.1002/nla.2326.
Quiring, Benjamin, & Vassilevski, Panayot S. Multilevel graph embedding. United States. doi:10.1002/nla.2326.
Quiring, Benjamin, and Vassilevski, Panayot S. Wed . "Multilevel graph embedding". United States. doi:10.1002/nla.2326.
@article{osti_1669230,
title = {Multilevel graph embedding},
author = {Quiring, Benjamin and Vassilevski, Panayot S.},
abstractNote = {The goal of the present paper is the design of embeddings of a general sparse graph into a set of points in $\mathbb{R}^d$ for appropriate d ≥ 2. The embeddings that we are looking at here aim to keep vertices that are grouped in communities together and keep the rest apart. To achieve this property, we utilize coarsening that respects possible community structures of the given graph. We employ a hierarchical multilevel coarsening approach that identifies communities (strongly connected groups of vertices) at every level. The multilevel strategy allows any given (presumably expensive) graph embedding algorithm to be made into a more scalable (and faster) algorithm. We demonstrate the presented approach on a number of given embedding algorithms and large-scale graphs and achieve speed-up over the methods in a recent paper.},
doi = {10.1002/nla.2326},
journal = {Numerical Linear Algebra with Applications},
number = ,
volume = ,
place = {United States},
year = {2020},
month = {9}
}

Journal Article:
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