EMPLOYING K-ARY n-CUBES FOR PARALLEL LAGRANGE INTERPOLATION

This paper proposes a parallel algorithm for computing anN( = Kn) point Lagrange interpolation on fc-ary n-cube networks. The algorithm consists of three phases: initialisation, main and final. There is no computation in the initialisation phase. The main phase is composed of N/2 steps, each consisting of four multiplications and four subtractions, and an additional step including one division and one multiplication. Communication in the main phase is based on an all-to-all broadcast algorithm on a Hamiltonian ring embedded in a k-ary n-cube. The final phase is carried out in n x ⌊k/l⌋ steps, each requiring one addition. A performance evaluation of the proposed algorithm reveals a near to optimum speedup for a typical range of sy:;tem parameters used in current state-of-the-art implementations. Our study also reveals that when implementation cost is taken into account low-dimensional K-ary n-cubes achieve better speedup than their higher-dimensional counterparts.