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<p>In this paper, we present a comprehensive study on the parallelization and optimization of Legendre Pairs (LPs) construction using High-Performance Computing (HPC) techniques. We address the computational challenges associated with LPs, particularly for large lengths, and propose a highly effective multi-GPU solution. Throughout this journey, we present our findings, insights, and contributions including the parallelized implementation of LP search using OpenMP, MPI, and CUDA, along with systematic optimization strategies for both CPU and GPU. We demonstrate significant performance improvements, achieving over 6500x and 1900x speedup on NVIDIA H100 and A30 GPUs, respectively, compared to the serial execution on Intel Xeon Gold 6338 CPU.</p>

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Efficient High-Performance Computing Strategies for the Legendre Pairs Search

  • 期刊论文

  • 发表日期：

    2026年5月16日

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  • Amirhossein Sojoodi,
  • Ilias S. Kotsireas,
  • Ahmad Afsahi

摘要

In this paper, we present a comprehensive study on the parallelization and optimization of Legendre Pairs (LPs) construction using High-Performance Computing (HPC) techniques. We address the computational challenges associated with LPs, particularly for large lengths, and propose a highly effective multi-GPU solution. Throughout this journey, we present our findings, insights, and contributions including the parallelized implementation of LP search using OpenMP, MPI, and CUDA, along with systematic optimization strategies for both CPU and GPU. We demonstrate significant performance improvements, achieving over 6500x and 1900x speedup on NVIDIA H100 and A30 GPUs, respectively, compared to the serial execution on Intel Xeon Gold 6338 CPU.