Parallel Lagrange interpolation on the star graph

Abstract

This paper introduces a parallel algorithm for computing an N=n!-point Lagrange interpolation on an n-star (n>2). It exploits several communication techniques on stars in a novel way which can be adapted for computing similar functions. The algorithm 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) sub-phases each with O(log n) steps where each step takes three communications and one addition.