Partitioning Spatially Located Computations Using Rectangles

Abstract

The ideal distribution of spatially located heterogeneous workloads is an important problem to address in parallel scientific computing. We investigate the problem of partitioning such workloads (represented as a matrix of positive 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, namely, rectilinear partitions, jagged partitions and hierarchical partitions. 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.