Parallel Lagrange interpolation on k-ary n-cubes with maximum channel utilization

Authors:
Aminollah Mahabadi;Hamid Sarbazi-Azad;Ebrahim Khodaie;Keivan Navi
Affiliations:
Department of Electrical and Computer Engineering, Shahed University, Tehran, Iran;Department of Computer Engineering, Sharif University of Technology, Tehran, Iran and School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran;National Organization for Educational Testing (NOET), Tehran, Iran;Faculty of Electrical and Computer Engineering, Beheshti University, Tehran, Iran
Venue:
The Journal of Supercomputing
Year:
2008

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Abstract

This paper proposes an efficient parallel algorithm for computing Lagrange interpolation on k-ary n-cube networks. This is done using the fact that a k-ary n-cube can be decomposed into n link-disjoint Hamiltonian cycles. Using these n link-disjoint cycles, we interpolate Lagrange polynomial using full bandwidth of the employed network. Communication in the main phase of the algorithm is based on an all-to-all broadcast algorithm on the n link-disjoint Hamiltonian cycles exploiting all network channels, and thus, resulting in high-efficiency in using network resources. A performance evaluation of the proposed algorithm reveals an optimum speedup for a typical range of system parameters used in current state-of-the-art implementations.