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Title: A Parallel Solver for Graph Laplacians

Abstract

Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as problem sizes increase and single core speeds stagnate, parallelism is essential to solve such problems quickly. We present an unsmoothed aggregation multigrid method for solving graph Laplacians in a distributed memory setting. We introduce new parallel aggregation and low degree elimination algorithms targeted specifically at irregular degree graphs. These algorithms are expressed in terms of sparse matrix-vector products using generalized sum and product operations. This formulation is amenable to linear algebra using arbitrary distributions and allows us to operate on a 2D sparse matrix distribution, which is necessary for parallel scalability. Our solver outperforms the natural parallel extension of the current state of the art in an algorithmic comparison. We demonstrate scalability to 576 processes and graphs with up to 1.7 billion edges.

Authors:
 [1];  [1]
  1. University of Colorado, Boulder (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1544266
Resource Type:
Conference
Resource Relation:
Conference: PASC '18 Proceedings of the Platform for Advanced Scientific Computing Conference, Basel, Switzerland, July 02 - 04, 2018
Country of Publication:
United States
Language:
English

Citation Formats

Konolige, Tristan, and Brown, Jed. A Parallel Solver for Graph Laplacians. United States: N. p., 2018. Web. doi:10.1145/3218176.3218227.
Konolige, Tristan, & Brown, Jed. A Parallel Solver for Graph Laplacians. United States. https://doi.org/10.1145/3218176.3218227
Konolige, Tristan, and Brown, Jed. 2018. "A Parallel Solver for Graph Laplacians". United States. https://doi.org/10.1145/3218176.3218227.
@article{osti_1544266,
title = {A Parallel Solver for Graph Laplacians},
author = {Konolige, Tristan and Brown, Jed},
abstractNote = {Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as problem sizes increase and single core speeds stagnate, parallelism is essential to solve such problems quickly. We present an unsmoothed aggregation multigrid method for solving graph Laplacians in a distributed memory setting. We introduce new parallel aggregation and low degree elimination algorithms targeted specifically at irregular degree graphs. These algorithms are expressed in terms of sparse matrix-vector products using generalized sum and product operations. This formulation is amenable to linear algebra using arbitrary distributions and allows us to operate on a 2D sparse matrix distribution, which is necessary for parallel scalability. Our solver outperforms the natural parallel extension of the current state of the art in an algorithmic comparison. We demonstrate scalability to 576 processes and graphs with up to 1.7 billion edges.},
doi = {10.1145/3218176.3218227},
url = {https://www.osti.gov/biblio/1544266}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2018},
month = {Mon Jan 01 00:00:00 EST 2018}
}

Conference:
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