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

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