A Parallel Solver for Graph Laplacians

Conference · Mon Jan 01 00:00:00 EST 2018

DOI:https://doi.org/10.1145/3218176.3218227· OSTI ID:1544266

Konolige, Tristan ^[1]; Brown, Jed ^[1]

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1. University of Colorado, Boulder (United States)

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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
• Sponsoring Organization: USDOE Office of Science (SC)
• OSTI ID: 1544266
• 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