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Title: Brief announcement: Hypergraph parititioning for parallel sparse matrix-matrix multiplication

Journal Article · · ACM Transactions on Parallel Computing
 [1];  [2];  [3];  [4]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  3. Univ. of California, Berkeley, CA (United States)
  4. Hebrew Univ., Jerusalem (Israel)
+ Show Author Affiliations

The performance of parallel algorithms for sparse matrix-matrix multiplication is typically determined by the amount of interprocessor communication performed, which in turn depends on the nonzero structure of the input matrices. In this paper, we characterize the communication cost of a sparse matrix-matrix multiplication algorithm in terms of the size of a cut of an associated hypergraph that encodes the computation for a given input nonzero structure. Obtaining an optimal algorithm corresponds to solving a hypergraph partitioning problem. Furthermore, our hypergraph model generalizes several existing models for sparse matrix-vector multiplication, and we can leverage hypergraph partitioners developed for that computation to improve application-specific algorithms for multiplying sparse matrices.

Research Organization:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1303161
Report Number(s):
SAND-2016-4718J; 640462
Journal Information:
ACM Transactions on Parallel Computing, Journal Name: ACM Transactions on Parallel Computing
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 12 works
Citation information provided by
Web of Science

References (8)

Communication optimal parallel multiplication of sparse random matrices conference January 2013
Hypergraph Partitioning for Automatic Memory Hierarchy Management conference November 2006
Simultaneous Input and Output Matrix Partitioning for Outer-Product--Parallel Sparse Matrix-Matrix Multiplication journal January 2014
Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid report September 2015
Graph Algorithms book January 1990
Parallel Sparse Matrix-Matrix Multiplication and Indexing: Implementation and Experiments journal January 2012
On Two-Dimensional Sparse Matrix Partitioning: Models, Methods, and a Recipe journal January 2010
Data management and query---Hypergraph partitioning for automatic memory hierarchy management conference January 2006

Cited By (16)

Embedded pattern formation by asynchronous robots without chirality journal May 2018
Distributed-Memory Tensor Completion for Generalized Loss Functions in Python using New Sparse Tensor Kernels preprint January 2019
Optimizing High Performance Markov Clustering for Pre-Exascale Architectures text January 2020
Simulating Population Protocols in Sub-Constant Time per Interaction text January 2020
Optimizing partitioned CSR-based SpGEMM on the Sunway TaihuLight journal March 2019
Privacy-Preserving Data Analytics book January 2018
A study on using uncertain time series matching algorithms for MapReduce applications: STATISTICAL PATTERN MATCHING ALGORITHMS FOR MAPREDUCE APPLICATIONS
  • Rizvandi, Nikzad Babaii; Taheri, Javid; Moraveji, Reza
  • Concurrency and Computation: Practice and Experience, Vol. 25, Issue 12 https://doi.org/10.1002/cpe.2895
journal July 2012
Large-Scale Indexing, Discovery, and Ranking for the Internet of Things (IoT) journal June 2018
A novel robust on-line protocol for load-balancing in structured peer-to-peer systems journal July 2012
Distributed MST and Routing in Almost Mixing Time
  • Ghaffari, Mohsen; Kuhn, Fabian; Su, Hsin-Hao
  • PODC '17: ACM Symposium on Principles of Distributed Computing, Proceedings of the ACM Symposium on Principles of Distributed Computing https://doi.org/10.1145/3087801.3087827
conference July 2017
Hypergraph Partitioning for Sparse Matrix-Matrix Multiplication preprint January 2016
Partitioning Models for Scaling Parallel Sparse Matrix-Matrix Multiplication journal April 2018
An Analysis Framework for Distributed Hierarchical Directories journal June 2013
On Counting the Population Size
  • Berenbrink, Petra; Kaaser, Dominik; Radzik, Tomasz
  • PODC '19: ACM Symposium on Principles of Distributed Computing, Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing https://doi.org/10.1145/3293611.3331631
conference July 2019
Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid report September 2015
Numerical algorithms for high-performance computational science
  • Dongarra, Jack; Grigori, Laura; Higham, Nicholas J.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2166 https://doi.org/10.1098/rsta.2019.0066
journal January 2020

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97 MATHEMATICS AND COMPUTING