A parallel algorithm for Lagrange interpolation on the star graph

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.