### Abstract

This paper introduces a new parallel algorithm for computing an N(= n!)-point Lagrange interpolation on an n-star (n > 2). The proposed algorithm exploits several communication techniques on stars in a novel way, which can be adapted for computing similar functions. It is optimal and consists of three phases: initialization, main, and final. While there is no computation in the initialization phase, the main phase is composed of n!/2 steps, each consisting of four multiplications, four subtractions, and one communication operation and an additional step including one division and one multiplication. The final phase is carried out in (n-1) subphases each with O(log n) steps where each step takes three communications and one addition. Results from a cost-performance comparative analysis reveal that for practical network sizes the new algorithm on the star exhibits superior performance over those proposed for common interconnection networks.

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

Pages (from-to) | 605-621 |

Number of pages | 17 |

Journal | Journal of Parallel and Distributed Computing |

Volume | 62 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2002 |

### Fingerprint

### Keywords

- Cost-performance analysis
- Hypercubes
- Interconnection networks
- Lagrange interpolation
- Parallel algorithms
- Speedup
- Star graph
- Tori

### ASJC Scopus subject areas

- Computer Science Applications
- Hardware and Architecture
- Control and Systems Engineering

### Cite this

*Journal of Parallel and Distributed Computing*,

*62*(4), 605-621. https://doi.org/10.1006/jpdc.2001.1812

**A parallel algorithm for Lagrange interpolation on the star graph.** / Sarbazi-Azad, H.; Ould-Khaoua, M.; Mackenzie, L. M.; Akl, S. G.

Research output: Contribution to journal › Article

*Journal of Parallel and Distributed Computing*, vol. 62, no. 4, pp. 605-621. https://doi.org/10.1006/jpdc.2001.1812

}

TY - JOUR

T1 - A parallel algorithm for Lagrange interpolation on the star graph

AU - Sarbazi-Azad, H.

AU - Ould-Khaoua, M.

AU - Mackenzie, L. M.

AU - Akl, S. G.

PY - 2002

Y1 - 2002

N2 - This paper introduces a new parallel algorithm for computing an N(= n!)-point Lagrange interpolation on an n-star (n > 2). The proposed algorithm exploits several communication techniques on stars in a novel way, which can be adapted for computing similar functions. It is optimal and consists of three phases: initialization, main, and final. While there is no computation in the initialization phase, the main phase is composed of n!/2 steps, each consisting of four multiplications, four subtractions, and one communication operation and an additional step including one division and one multiplication. The final phase is carried out in (n-1) subphases each with O(log n) steps where each step takes three communications and one addition. Results from a cost-performance comparative analysis reveal that for practical network sizes the new algorithm on the star exhibits superior performance over those proposed for common interconnection networks.

AB - This paper introduces a new parallel algorithm for computing an N(= n!)-point Lagrange interpolation on an n-star (n > 2). The proposed algorithm exploits several communication techniques on stars in a novel way, which can be adapted for computing similar functions. It is optimal and consists of three phases: initialization, main, and final. While there is no computation in the initialization phase, the main phase is composed of n!/2 steps, each consisting of four multiplications, four subtractions, and one communication operation and an additional step including one division and one multiplication. The final phase is carried out in (n-1) subphases each with O(log n) steps where each step takes three communications and one addition. Results from a cost-performance comparative analysis reveal that for practical network sizes the new algorithm on the star exhibits superior performance over those proposed for common interconnection networks.

KW - Cost-performance analysis

KW - Hypercubes

KW - Interconnection networks

KW - Lagrange interpolation

KW - Parallel algorithms

KW - Speedup

KW - Star graph

KW - Tori

UR - http://www.scopus.com/inward/record.url?scp=0036113979&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036113979&partnerID=8YFLogxK

U2 - 10.1006/jpdc.2001.1812

DO - 10.1006/jpdc.2001.1812

M3 - Article

VL - 62

SP - 605

EP - 621

JO - Journal of Parallel and Distributed Computing

JF - Journal of Parallel and Distributed Computing

SN - 0743-7315

IS - 4

ER -