PARS3: Parallel Sparse Skew-Symmetric Matrix-Vector Multiplication with Reverse Cuthill-McKee Reordering

TL;DR

This paper introduces a novel parallel skew-symmetric sparse matrix-vector multiplication method using RCM reordering to transform matrices into band form, achieving significant speedups over serial implementations.

Contribution

First implementation of parallel skew-symmetric SpMV kernels utilizing RCM reordering to optimize matrix structure for parallel processing.

Findings

Achieved up to 19x speedup over serial implementation.

Effectively used RCM reordering to transform matrices into band form.

Outperformed heuristic graph-coloring approaches in parallel SpMV.

Abstract

Sparse matrices, as prevalent primitive of various scientific computing algorithms, persist as a bottleneck in processing. A skew-symmetric matrix flips signs of symmetric pairs in a symmetric matrix. Our work, Parallel 3-Way Banded Skew-Symmetric Sparse Matrix-Vector Multiplication, equally improves parallel symmetric SpMV kernels with a different perspective than the common literature trends, by manipulating the form of matrix in a preprocessing step to accelerate the repeated computations of iterative solvers. We effectively use Reverse Cuthill-McKee (RCM) reordering algorithm to transform a sparse skew-symmetrix matrix into a band matrix, then efficiently parallelize it by splitting the band structure into 3 different parts by considering its local sparsity. Our proposed method with RCM is novel in the sense that it is the first implementation of parallel skew-symmetric SpMV kernels. Our enhancements in SpMV and findings are valuable with significant strong scalings of up to 19x over the serial compressed SpMV implementation. We overperform a heuristic-based graph-coloring approach with synchronization phases in implementing parallel symmetric SpMVs. Our approach also naturally applies to parallel sparse symmetric SpMVs, that can inspire widespread SpMV solutions to adapt presented optimizations in this paper.