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.

翻译：负载均衡划分是并行化各类计算的关键初始步骤。本文提出SGORP——一种基于次梯度优化的新型空间划分方法，用于求解$d$维直线划分问题（RPP）。该方法支持自定义目标函数，同时可施加特定用户约束（例如选定维度上的对称划分）。通过600余个测试矩阵的广泛实验评估表明，该算法在性能上优于当前最先进的RPP及对称RPP算法。此外，我们以三角计数与稀疏矩阵乘法（SpGEMM）两项应用为例，将其负载均衡问题建模为$3$维RPP，验证了算法在应用特定负载均衡中的有效性。