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Distributing spatially located heterogeneous workloads is an importantproblem in parallel scientific computing. We investigate the problem ofpartitioning such workloads (represented as a matrix of non-negative integers)into rectangles, such that the load of the most loaded rectangle (processor) isminimized. Since finding the optimal arbitrary rectangle-based partition is anNP-hard problem, we investigate particular classes of solutions: rectilinear,jagged and hierarchical. We present a new class of solutions called m-wayjagged partitions, propose new optimal algorithms for m-way jagged partitionsand hierarchical partitions, propose new heuristic algorithms, and provideworst case performance analyses for some existing and new heuristics. Moreover,the algorithms are tested in simulation on a wide set of instances. Resultsshow that two of the algorithms we introduce lead to a much better load balancethan the state-of-the-art algorithms. We also show how to design a two-phasealgorithm that reaches different time/quality tradeoff.

Load-Balancing Spatially Located Computations using Rectangular Partitions