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Parallel numerical interpolation on necklace hypercubes

Meraji, S ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. DOI: 10.1109/AMS.2007.78
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2007
  4. Abstract:
  5. The Necklace Hypecube has been recently proposed as an attractive topology for multicomputers and was shown to have many desirable properties such as well-scalability and suitability for VLSI implementation. This paper introduces a parallel algorithm for computing an N-point Lagrange interpolation on a necklace hypercube multiprocessor. This algorithm consists of 3 phases: initialization, main and final. There is no computation in the initialization phase. The main phase consists of [E/2] steps (with E being the number of edges of the network), each consisting of 4 multiplications and 4 subtractions, and an additional step including 1 division and 1 multiplication. Communication in the main phase is based on an all-to-all broadcast algorithm using some Eulerian rings embedded in the host necklace hypercube. The final phase is carried out in three sub-phases. There are [k/2] steps in the first sub-phase where k is the size of necklace. Each of sub-phases two and three contains n steps. Our study reveals that when implementation cost in taken into account, there is no speedup difference between lowdimensional and high-dimensional necklace networks. © 2007 IEEE
  6. Keywords:
  7. Geometry ; Interpolation ; All-to-all broadcast ; High-dimensional ; Hypercube multiprocessors ; Implementation cost ; Lagrange interpolations ; Multicomputers ; Numerical interpolations ; VLSI implementation ; Hypercube networks
  8. Source: 1st Asia International Conference on Modelling and Simulation - Asia Modelling Symposium 2007, AMS 2007, 27 March 2007 through 30 March 2007 ; 2007 , Pages 123-127 ; 0769528457 (ISBN); 9780769528458 (ISBN)
  9. URL: https://ieeexplore.ieee.org/document/4148645