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Top-K and selection operations are critical in data processing and analysis, and their efficient implementation on GPUs is increasingly important due to the growing demands of data analysis. Existing methods, primarily relying on the bucket partition execution model, encounter challenges such as uneven bucket distribution and latency in merging processes. To address these issues, we introduce a novel Split-Bucket Partition (SBP) execution model that specifically addresses these challenges. Additionally, we propose task and control flow optimizations targeted at top-K and selection algorithms, which further contribute to performance improvements. Our optimized algorithms significantly outperform existing approaches, delivering performance gains of up to 2.3 times and 1.6 times for different bucket partitioning rules. Our algorithms show robust performance improvements in non-uniform data scenarios, with gains ranging from 1.9 times to 15.5 times. However, it should be noted that the SBP model has limitations related to shared memory and register utilization, potentially impacting performance. Tests on TU102 and A100 GPU architectures validate the effectiveness of our approach, achieving a maximum speedup of 2.9 times. The study suggests that while the SBP model is effective for top-K and selection algorithms, it also holds promise for other computational tasks, setting the stage for future research. [ABSTRACT FROM AUTHOR]

Sparse matrix-vector multiplication (SpMV) plays a critical role in a wide range of linear algebra computations, particularly in scientific and engineering disciplines. However, the irregular memory access patterns, extensive memory usage, high bandwidth requirements, and underutilization of parallelism hinder the computational efficiency of SpMV on GPUs. In this paper, we propose a novel approach called block-wise dynamic mixed-precision (BDMP) to address these challenges. Our methodology involves partitioning the original matrix into uniformly sized blocks, with each block's size determined by considering architectural characteristics and accuracy requirements. Additionally, we dynamically assign precision to each block using a precision selection method that takes into account the value distribution of the original sparse matrix. We develop two distinct SpMV computation algorithms for BDMP: BDMP-PBP (Precision-based partitioning) and BDMP-TCKI (Tailored compression and kernel implementation). BDMP-PBP partitions the matrix into two independent matrices for separate computations based on block precision, offering flexibility for integration with other optimization techniques. Meanwhile, BDMP-TCKI focuses on achieving significant thread-level parallelism and memory utilization by tailoring an appropriate compressed storage format and kernel implementation for each block. We compare BDMP with NVIDIA's cuSPARSE library and three state-of-the-art SpMV methods, including SELLP, MergeBase, and BalanceCSR, using matrices from the University of Florida's SuiteSparse dataset collection. BDMP-PBP and BDMP-TCKI show average speedups up to 2.64 × and 2.91 × on Turing RTX 2080Ti, and up to 2.99 × and 3.22 × on Ampere A100. The results demonstrate that BDMP enables the optimization of computation speed without compromising the precision necessary for reliable results. [ABSTRACT FROM AUTHOR]