### Abstract

We present and evaluate, for the first time, a parallel algorithm for solving the LU decomposition problem on the star graph. The proposed parallel algorithm is of O(N ^{3}/n!) computation complexity and uses O(Nn) communication time to decompose a matrix of order N on a star graph of dimension n, where N≥(n - 1)!. The incurred communication time is better than the best known results for the hypercube, O(N log n!), and the mesh, O(N√n!), each with approximately n! nodes. The proposed parallel algorithm takes advantage of the attractive topological qualities of the star graph in order to reduce the communication time involved in tasks such as pivoting, row/column interchanges, and pivot row and multipliers column broadcasts.

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

Pages (from-to) | 803-812 |

Number of pages | 10 |

Journal | IEEE Transactions on Parallel and Distributed Systems |

Volume | 8 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1997 |

### Fingerprint

### Keywords

- Interconnection networks
- Matrix decomposition
- Parallel processing
- Star graphs

### ASJC Scopus subject areas

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

### Cite this

*IEEE Transactions on Parallel and Distributed Systems*,

*8*(8), 803-812. https://doi.org/10.1109/71.605767

**Matrix decomposition on the star graph.** / Al-Ayyoub, Abdel Elah; Day, Khaled.

Research output: Contribution to journal › Article

*IEEE Transactions on Parallel and Distributed Systems*, vol. 8, no. 8, pp. 803-812. https://doi.org/10.1109/71.605767

}

TY - JOUR

T1 - Matrix decomposition on the star graph

AU - Al-Ayyoub, Abdel Elah

AU - Day, Khaled

PY - 1997

Y1 - 1997

N2 - We present and evaluate, for the first time, a parallel algorithm for solving the LU decomposition problem on the star graph. The proposed parallel algorithm is of O(N 3/n!) computation complexity and uses O(Nn) communication time to decompose a matrix of order N on a star graph of dimension n, where N≥(n - 1)!. The incurred communication time is better than the best known results for the hypercube, O(N log n!), and the mesh, O(N√n!), each with approximately n! nodes. The proposed parallel algorithm takes advantage of the attractive topological qualities of the star graph in order to reduce the communication time involved in tasks such as pivoting, row/column interchanges, and pivot row and multipliers column broadcasts.

AB - We present and evaluate, for the first time, a parallel algorithm for solving the LU decomposition problem on the star graph. The proposed parallel algorithm is of O(N 3/n!) computation complexity and uses O(Nn) communication time to decompose a matrix of order N on a star graph of dimension n, where N≥(n - 1)!. The incurred communication time is better than the best known results for the hypercube, O(N log n!), and the mesh, O(N√n!), each with approximately n! nodes. The proposed parallel algorithm takes advantage of the attractive topological qualities of the star graph in order to reduce the communication time involved in tasks such as pivoting, row/column interchanges, and pivot row and multipliers column broadcasts.

KW - Interconnection networks

KW - Matrix decomposition

KW - Parallel processing

KW - Star graphs

UR - http://www.scopus.com/inward/record.url?scp=0031211451&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031211451&partnerID=8YFLogxK

U2 - 10.1109/71.605767

DO - 10.1109/71.605767

M3 - Article

VL - 8

SP - 803

EP - 812

JO - IEEE Transactions on Parallel and Distributed Systems

JF - IEEE Transactions on Parallel and Distributed Systems

SN - 1045-9219

IS - 8

ER -