Segmented Reduction Algorithm for Sparse Matrix Workload Balancing
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Solution Overview
Problem
Sparse matrix multiplication, particularly in applications like graphics processing, faces challenges in mapping reduction operations to data-parallel machines due to unequal workload distribution when rows of the matrix are mapped onto processing elements.
Innovation Solution
Converting reduction algorithms to segmented reduction algorithms, allowing for parallel processing across arbitrary partitions of the input vector, thereby avoiding workload imbalances and optimizing performance by utilizing parallel processing architectures like GPUs and SIMD architectures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If reduction operations are mapped to data-parallel machines using traditional methods, then processing can be performed in parallel, but unequal workload distribution occurs causing inefficiency
Solution Approach 1:
The input vector is divided into multiple segments that are processed in parallel by different processing elements. Each segment is independently reduced, and the partial results are combined to produce the final result. This segmentation allows for better load distribution across processing elements while maintaining parallel processing capability.
2Productivity
If traditional segmented scans are used for sparse matrix-vector multiplication, then parallel processing is achieved, but computational efficiency is reduced by computing unnecessary values
Solution Approach 1:
The algorithm extracts and processes only the non-zero elements and their corresponding indices from the sparse matrix representation. By identifying and working solely with relevant data elements rather than processing entire segments uniformly, the algorithm avoids computing unnecessary values and reduces wasted computational effort.
Solution Approach 2:
Instead of performing complete segmented scans on entire vector segments, the algorithm performs partial reduction operations only on the necessary portions of data that contribute to the final result. This partial action approach computes only what is required, avoiding excessive computation on irrelevant elements.
Data Source
AI summary
A system, method, and computer program product are provided for converting a reduction algorithm to a segmented reduction algorithm. In operation, a reduction algorithm is identified. Additionally, the reduction algorithm is converted to a segmented reduction algorithm. Furthermore, the segmented reduction algorithm is performed to produce an output.