SGORP：一种基于次梯度的d维直线划分方法
SGORP: A Subgradient-based Method for d-Dimensional Rectilinear Partitioning
AI总结：
本文提出基于次梯度优化的d维直线划分方法SGORP，支持定制目标与约束，在600余测试矩阵上性能优于现有最优算法，且可有效处理三角形计数、SpGEMM等应用的三维负载均衡问题。
摘要：
负载均衡划分是并行化各类计算的关键首要步骤。本文提出一种基于次梯度优化的新型空间划分方法SGORP，用于求解d维直线划分问题（RPP）。该方法支持使用可定制的目标函数，以及部分用户指定约束，例如选定维度上的对称划分。基于600余个测试矩阵的大量实验评估表明，该算法相较现有最优RPP与对称RPP算法取得了优异性能。此外，本文以三角形计数和稀疏矩阵乘法（SpGEMM）两个应用为案例，将其负载均衡问题建模为三维RPP，验证了该算法在特定应用负载均衡中的有效性。
英文摘要：
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.
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