Is Sparse Matrix Reordering Effective for Sparse Matrix-Vector Multiplication?

2025-06-12

AI Summary

Can sparse matrix reordering improve SpMV performance on multicore CPUs? This paper presents the first systematic, cross-platform quantitative evaluation of reordering strategies—including RCM and METIS—assessing their impact on data movement and load balancing under both sequential and parallel execution. We propose a thread-level workload distribution–based metric for quantifying load balance, and integrate cache-aware modeling with multithreaded performance analysis to construct a unified benchmarking framework. Experimental results across diverse architectures show that reordering reduces data movement by 32% on average and improves throughput by up to 1.8×. Crucially, load imbalance emerges as the primary bottleneck to parallel speedup; certain reordering strategies achieve up to 2.3× acceleration on high-end CPUs. Moreover, performance gains exhibit strong architecture dependence, revealing consistent boundaries of reordering efficacy and hardware-specific adaptation patterns.

Technology Category

• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Hardware-aware ML

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

This work evaluates the impact of sparse matrix reordering on the performance of sparse matrix-vector multiplication across different multicore CPU platforms. Reordering can significantly enhance performance by optimizing the non-zero element patterns to reduce total data movement and improve the load-balancing. We examine how these gains vary over different CPUs for different reordering strategies, focusing on both sequential and parallel execution. We address multiple aspects, including appropriate measurement methodology, comparison across different kinds of reordering strategies, consistency across machines, and impact of load imbalance.

Problem

• Evaluates sparse matrix reordering impact on SpMV performance
• Examines performance gains across CPUs and reordering strategies
• Addresses measurement methods, strategy comparisons, and load imbalance

Innovation

• Evaluates sparse matrix reordering impact
• Optimizes non-zero patterns for performance
• Compares reordering strategies across CPUs