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Hypergraph Partitioning for Sparse Matrix-Matrix Multiplication by Grey Ballard; Alex Druinsky; Nicholas Knight; Oded Schwartz is a Computer Science article available to read on EtoBox.

What is Hypergraph Partitioning for Sparse Matrix-Matrix Multiplication about?

We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance is often communication bound. This model correctly describes both the interprocessor communication volume along a critical path in a parallel computation and also the volume of data moving through the memory hierarchy in a sequential computation. We show that identifying a communication-optimal algorithm for particular input matrices is equivalent to solving a hypergraph partitioning problem. Our approach is nonzero structure dependent, meaning that we seek the best algorithm for the given input matrices. In addition to our three-dimensional fine-grained model, we also propose coarse-grained one-dimensional and two-dimensional models that correspond to simpler SpGEMM algorithms. We explore the relations between our models theoretically, and we study their performance experimentally in the context of three applications that use SpGEMM as a key computation. For each application, we find that at least one coarse-grained model is as communication efficient as the fine-grained model. We also observe that diffe

Who reads Hypergraph Partitioning for Sparse Matrix-Matrix Multiplication?

Author

Grey Ballard; Alex Druinsky; Nicholas Knight; Oded Schwartz

Publisher

ACM

Published

2016

Language

EN

Field

Computer Science (Physical Sciences)