A parallel algorithm for Lagrange interpolation on the star graph

  • Authors:

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

  • Affiliations:

  • Department of Computing Science, University of Glasgow, Glasgow G12 8RZ, United Kingdom;Department of Computing Science, University of Glasgow, Glasgow G12 8RZ, United Kingdom;Department of Computing Science, University of Glasgow, Glasgow G12 8RZ, United Kingdom;Department of Computer and Information Science, Queen's University, Kingston, Ontario, Canada

  • Venue:
  • Journal of Parallel and Distributed Computing
  • Year:
  • 2002

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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.