### 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 |
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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 |

### 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

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## Cite this

*Journal of Parallel and Distributed Computing*,

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