### Abstract

Most common multicomputer networks, e.g. d-ary h-cubes, are graph topologies where an edge (channel) interconnects exactly two vertices (nodes). Hypergraphs are a generalisation of the graph model, where a channel interconnects an arbitrary number of nodes. Previous studies have used synthetic workloads (e.g. statistical distributions) to stress the superior performance characteristics of regular multi-dimensional hypergraphs, also known as hypermeshes, over d-ary h-cubes. There has been, however, hardly any study that has considered real-world parallel applications. This paper contributes towards filling this gap by providing a comparative study of the performance of one of the most common numerical problems, namely matrix factorisation, on the hypermesh, hypercube, and d-ary h-cube, To this end, the paper first introduces orthogonal networks as a unified model for describing both the graph and hypergraph topologies. It then develops a generalised parallel algorithm for matrix factorisation and evaluates its performance on the hypermesh, hypercube and d-ary h-cube. The results reveal that the hypermesh supports matrix computation more efficiently, and therefore provides more evidence of the hypermesh as a viable network for future large-scale multicomputers.

Original language | English |
---|---|

Pages (from-to) | 37-53 |

Number of pages | 17 |

Journal | Journal of Supercomputing |

Volume | 20 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 2001 |

### Fingerprint

### Keywords

- Gaussian elimination
- Hypermeshes
- Interconnection networks
- Matrix factorization
- Multicomputers
- Orthogonal networks
- Performance analysis

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Hardware and Architecture
- Theoretical Computer Science
- Computational Theory and Mathematics

### Cite this

*Journal of Supercomputing*,

*20*(1), 37-53. https://doi.org/10.1023/A:1011140203528

**On the performance of parallel matrix factorisation on the hypermesh.** / Al-Ayyoub, A.; Ould-Khaoua, M.; Day, K.

Research output: Contribution to journal › Article

*Journal of Supercomputing*, vol. 20, no. 1, pp. 37-53. https://doi.org/10.1023/A:1011140203528

}

TY - JOUR

T1 - On the performance of parallel matrix factorisation on the hypermesh

AU - Al-Ayyoub, A.

AU - Ould-Khaoua, M.

AU - Day, K.

PY - 2001/8

Y1 - 2001/8

N2 - Most common multicomputer networks, e.g. d-ary h-cubes, are graph topologies where an edge (channel) interconnects exactly two vertices (nodes). Hypergraphs are a generalisation of the graph model, where a channel interconnects an arbitrary number of nodes. Previous studies have used synthetic workloads (e.g. statistical distributions) to stress the superior performance characteristics of regular multi-dimensional hypergraphs, also known as hypermeshes, over d-ary h-cubes. There has been, however, hardly any study that has considered real-world parallel applications. This paper contributes towards filling this gap by providing a comparative study of the performance of one of the most common numerical problems, namely matrix factorisation, on the hypermesh, hypercube, and d-ary h-cube, To this end, the paper first introduces orthogonal networks as a unified model for describing both the graph and hypergraph topologies. It then develops a generalised parallel algorithm for matrix factorisation and evaluates its performance on the hypermesh, hypercube and d-ary h-cube. The results reveal that the hypermesh supports matrix computation more efficiently, and therefore provides more evidence of the hypermesh as a viable network for future large-scale multicomputers.

AB - Most common multicomputer networks, e.g. d-ary h-cubes, are graph topologies where an edge (channel) interconnects exactly two vertices (nodes). Hypergraphs are a generalisation of the graph model, where a channel interconnects an arbitrary number of nodes. Previous studies have used synthetic workloads (e.g. statistical distributions) to stress the superior performance characteristics of regular multi-dimensional hypergraphs, also known as hypermeshes, over d-ary h-cubes. There has been, however, hardly any study that has considered real-world parallel applications. This paper contributes towards filling this gap by providing a comparative study of the performance of one of the most common numerical problems, namely matrix factorisation, on the hypermesh, hypercube, and d-ary h-cube, To this end, the paper first introduces orthogonal networks as a unified model for describing both the graph and hypergraph topologies. It then develops a generalised parallel algorithm for matrix factorisation and evaluates its performance on the hypermesh, hypercube and d-ary h-cube. The results reveal that the hypermesh supports matrix computation more efficiently, and therefore provides more evidence of the hypermesh as a viable network for future large-scale multicomputers.

KW - Gaussian elimination

KW - Hypermeshes

KW - Interconnection networks

KW - Matrix factorization

KW - Multicomputers

KW - Orthogonal networks

KW - Performance analysis

UR - http://www.scopus.com/inward/record.url?scp=0035425980&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035425980&partnerID=8YFLogxK

U2 - 10.1023/A:1011140203528

DO - 10.1023/A:1011140203528

M3 - Article

VL - 20

SP - 37

EP - 53

JO - Journal of Supercomputing

JF - Journal of Supercomputing

SN - 0920-8542

IS - 1

ER -