Distributing spatially located heterogeneous workloads is an important problem in parallel scientific computing. We investigate the problem of partitioning such workloads (represented as a matrix of non-negative integers) into rectangles, such that the load of the most loaded rectangle (processor) is minimized. Since finding the optimal arbitrary rectangle-based partition is an NP-hard problem, we investigate particular classes of solutions: rectilinear, jagged and hierarchical. We present a new class of solutions called m-way jagged partitions, propose new optimal algorithms for m-way jagged partitions and hierarchical partitions, propose new heuristic algorithms, and provide worst case performance analyses for some existing and new heuristics. Moreover, the algorithms are tested in simulation on a wide set of instances. Results show that two of the algorithms we introduce lead to a much better load balance than the state-of-the-art algorithms. We also show how to design a two-phase algorithm that reaches different time/quality tradeoff.
@article{arxiv.1104.2566,
title = {Load-Balancing Spatially Located Computations using Rectangular Partitions},
author = {Erik Saule and Erdeniz Ö. Baş and Ümit V. Çatalyürek},
journal= {arXiv preprint arXiv:1104.2566},
year = {2011}
}