A Parallel Algorithm for Lagrange Interpolation on the Star Graph

✍ Scribed by H. Sarbazi-Azad; M. Ould-Khaoua; L.M. Mackenzie; S.G. Akl

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 226 KB
• Volume: 62
• Category: Article
• ISSN: 0743-7315
• DOI: 10.1006/jpdc.2001.1812

✦ Synopsis

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.