Load-balancing spatially located computations using rectangular partitions

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 tradeoffs.

► Models spatially located computation as a load matrix.
► Parallelization is obtained by partitioning the matrix in balanced rectangles.
► Introduces new classes of rectangular partition, heuristic and optimal algorithms.
► Experimentally shows that two proposed heuristics outperform known algorithms.
► Introduces a two-phase hybrid algorithm to achieve more time/quality tradeoffs.