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High-performance CGM-based parallel algorithms for minimum cost parenthesizing problem

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Abstract

Minimum cost parenthesizing problem (MPP for short) is a well-known example of the polyadic-nonserial dynamic-programming problem. This paper presents two efficient parallel algorithms on the coarse-grained multicomputer model for solving the MPP. By allowing processors to stay active as long as possible thanks to our irregular partitioning technique of dependency graph, these algorithms minimize their idle time and promote load-balancing between them. The algorithms also reduce the latency time of processors (which is the largest part of the overall communication time) by allowing them to start evaluating subproblems as soon as the data they need are available. The first algorithm runs in \({\mathcal {O}}\left( n^3/4^k p \right)\) execution time with \({\mathcal {O}}\left( 2^k \sqrt{p}\right)\) communication rounds. The second runs in \({\mathcal {O}}\left( n^3/2^k p \right)\) execution time with \({\mathcal {O}}\left( 4^k \sqrt{p}\right)\) communication rounds. n is the input data size, p is the number of processors, and k is a parameter used in the partitioning technique of our algorithms. The experimental results obtained show that these new algorithms are better than the most efficient previous solutions.

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Notes

  1. It is the level (step) involving a maximum number of blocks.

  2. Matrix-multiplication \((+, min)\) is a matrix multiplication in which the multiplication and summation operations are replaced by addition and the minimum, respectively.

  3. https://www.u-picardie.fr/recherche/presentation/plateformes/plateforme-matrics-382844.kjsp.

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Acknowledgements

The authors wish to express their gratitude to the University of Picardie Jules Verne which made it possible to carry out the experimentations of this work.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Dschang, Dschang, Cameroon

    Jerry Lacmou Zeutouo & Vianney Kengne Tchendji

  2. Computer Science Lab-MIS, University of Picardie Jules Verne, Amiens, France

    Jean Frédéric Myoupo

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  1. Jerry Lacmou Zeutouo
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Correspondence to Vianney Kengne Tchendji.

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Lacmou Zeutouo, J., Kengne Tchendji, V. & Myoupo, J.F. High-performance CGM-based parallel algorithms for minimum cost parenthesizing problem. J Supercomput 78, 5306–5332 (2022). https://doi.org/10.1007/s11227-021-04069-9

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