Heuristics for Symmetric Rectilinear Matrix Partitioning

TL;DR

This paper introduces five heuristics for symmetric rectilinear partitioning of square sparse matrices, aiming to optimize tiled execution in matrix and graph analytics, with thorough experimental validation.

Contribution

It proposes novel heuristics specifically designed for symmetric rectilinear partitioning of square matrices, addressing a gap in existing methods.

Findings

Heuristics significantly improve partition quality over baseline methods.

Experimental results demonstrate effectiveness across various matrix types.

Symmetric partitioning benefits tiled execution efficiency.

Abstract

Partitioning sparse matrices and graphs is a common and important problem in many scientific and graph analytics applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as generalized block distribution) of sparse matrices, which is needed for tiled (or {\em blocked}) execution of sparse matrix and graph analytics kernels. More specifically, in this work, we address the problem of symmetric rectilinear partitioning of square matrices. By symmetric, we mean having the same partition on rows and columns of the matrix, yielding a special tiling where the diagonal tiles (blocks) will be squares. We propose five heuristics to solve two different variants of this problem, and present a thorough experimental evaluation showing the effectiveness of the proposed algorithms.