SGORP: A Subgradient-based Method for d-Dimensional Rectilinear Partitioning

TL;DR

SGORP is a novel subgradient optimization-based spatial partitioning method for d-dimensional rectilinear partitioning, effectively balancing load in parallel computations with customizable objectives and constraints.

Contribution

The paper introduces SGORP, a new method for d-dimensional rectilinear partitioning that supports user-specific constraints and outperforms existing algorithms in load balancing tasks.

Findings

Achieves better performance than state-of-the-art algorithms.

Effectively balances load for applications like Triangle Counting and SpGEMM.

Demonstrates versatility in application-specific load balancing.

Abstract

Partitioning for load balancing is a crucial first step to parallelize any type of computation. In this work, we propose SGORP, a new spatial partitioning method based on Subgradient Optimization, to solve the $d$-dimensional Rectilinear Partitioning Problem (RPP). Our proposed method allows the use of customizable objective functions as well as some user-specific constraints, such as symmetric partitioning on selected dimensions. Extensive experimental evaluation using over 600 test matrices shows that our algorithm achieves favorable performance against the state-of-the-art RPP and Symmetric RPP algorithms. Additionally, we show the effectiveness of our algorithm to do application-specific load balancing using two applications as motivation: Triangle Counting and Sparse Matrix Multiplication (SpGEMM), where we model their load-balancing problems as $3$-dimensional RPPs.