A parallel algorithm for Lagrange interpolation on the star graph

H. Sarbazi-Azad, M. Ould-Khaoua, L. M. Mackenzie, S. G. Akl

Research output: Contribution to journalArticle

15 Citations (Scopus)

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 languageEnglish
Pages (from-to)605-621
Number of pages17
JournalJournal of Parallel and Distributed Computing
Volume62
Issue number4
DOIs
Publication statusPublished - 2002

Fingerprint

Star Graph
Lagrange Interpolation
Parallel algorithms
Parallel Algorithms
Stars
Interpolation
Star
Communication
Initialization
Multiplication
Computing
Interconnection Networks
Subtraction
Comparative Analysis
Performance Analysis
Division
Costs

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

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

In: Journal of Parallel and Distributed Computing, Vol. 62, No. 4, 2002, p. 605-621.

Research output: Contribution to journalArticle

Sarbazi-Azad, H. ; Ould-Khaoua, M. ; Mackenzie, L. M. ; Akl, S. G. / A parallel algorithm for Lagrange interpolation on the star graph. In: Journal of Parallel and Distributed Computing. 2002 ; Vol. 62, No. 4. pp. 605-621.
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