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An efficient coarse-grain multicomputer algorithm for the minimum cost parenthesizing problem

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Abstract

Several problems modeled by dynamic programming have been solved using a coarse-grain multicomputer parallel model (CGM for short). These problems use either polyadic dynamic programming or monadic non-serial dynamic programming. In this paper, we address the general case: we propose a parallel algorithm in the CGM model with p processors for the Optimal String Parenthesizing Problem or Minimum Cost Parenthesizing Problem, which is a typical polyadic non-serial dynamic programming problem. The algorithm we obtain requires ⌈(2p)1/2⌉ communication rounds and, at most, O(n 3/p) time-steps on p processors. This new CGM algorithm performs better than the previously most efficient solution, which uses p communication rounds.

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Authors and Affiliations

  1. University of Yaounde 1, Yaounde, Cameroon

    Vianney Kengne Tchendji

  2. Université de Picardie-Jules Verne, 33 rue Saint Leu, 80028, Amiens, France

    Jean Frédéric Myoupo

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  1. Vianney Kengne Tchendji
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Correspondence to Jean Frédéric Myoupo.

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Kengne Tchendji, V., Myoupo, J.F. An efficient coarse-grain multicomputer algorithm for the minimum cost parenthesizing problem. J Supercomput 61, 463–480 (2012). https://doi.org/10.1007/s11227-011-0601-9

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