Efficient Distributed Transposition Of Large-Scale Multigraphs And High-Cardinality Sparse Matrices
2020
Graph-based representations underlie a wide range of scientific problems.
Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating distinct subsets of rows to compute nodes.
Efficient matrix transpose is an operation of high importance, providing the reverse graph pathways and a column-ordered matrix view. This operation is well studied for simple graph models. Nevertheless, its resolution for multigraphs and higher-cardinality connectivity matrices is unexistent.
We advance state-of-the-art distributed transposition methods by providing a theoretical model, algorithmic details, MPI-based implementation and proof of mathematical soundness for such complex models. Benchmark results demonstrate ideal and almost ideal scaling properties for perfectly- and heterogeneously-balanced datasets, respectively
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